28-Mar-2019 12:32:16 test_int_test MATLAB version Test test_int. TEST01 Composite midpoint rule, for 1D finite interval problems. Problem Exact Ints Approx Error 1 1.718282 1 1.648721 6.956056e-02 2 1.700513 1.776911e-02 4 1.713815 4.466549e-03 8 1.717164 1.118163e-03 16 1.718002 2.796364e-04 32 1.718212 6.991508e-05 64 1.718264 1.747914e-05 128 1.718277 4.369809e-06 2 0.700000 1 1.000000 3.000000e-01 2 0.500000 2.000000e-01 4 0.750000 5.000000e-02 8 0.750000 5.000000e-02 16 0.687500 1.250000e-02 32 0.687500 1.250000e-02 64 0.703125 3.125000e-03 128 0.703125 3.125000e-03 3 0.666667 1 0.707107 4.044011e-02 2 0.683013 1.634604e-02 4 0.672977 6.310730e-03 8 0.669032 2.365505e-03 16 0.667537 8.700090e-04 32 0.666983 3.160198e-04 64 0.666781 1.138365e-04 128 0.666707 4.077399e-05 4 0.479428 1 -0.160000 6.394282e-01 2 0.319667 1.597616e-01 4 0.439407 4.002084e-02 8 0.469417 1.001159e-02 16 0.476925 2.503317e-03 32 0.478802 6.258557e-04 64 0.479272 1.564656e-04 128 0.479389 3.911650e-05 5 1.582233 1 2.222222 6.399893e-01 2 1.649485 6.725157e-02 4 1.596905 1.467173e-02 8 1.585943 3.709729e-03 16 1.583162 9.286311e-04 32 1.582465 2.322191e-04 64 1.582291 5.805841e-05 128 1.582247 1.451483e-05 6 1.460447 1 1.414214 4.623357e-02 2 1.000000 4.604471e-01 4 1.492030 3.158256e-02 8 1.472775 1.232775e-02 16 1.465103 4.656349e-03 32 1.462168 1.721271e-03 64 1.461074 6.273476e-04 128 1.460674 2.264998e-04 7 2.000000 1 1.414214 5.857864e-01 2 1.577350 4.226497e-01 4 1.698844 3.011559e-01 8 1.786461 2.135390e-01 16 1.848857 1.511433e-01 32 1.893088 1.069116e-01 64 1.924393 7.560724e-02 128 1.946535 5.346472e-02 8 0.866973 1 0.941176 7.420348e-02 2 0.877876 1.090345e-02 4 0.869605 2.632419e-03 8 0.867626 6.528211e-04 16 0.867136 1.628717e-04 32 0.867014 4.069706e-05 64 0.866983 1.017296e-05 128 0.866976 2.543159e-06 9 1.154701 1 1.000000 1.547005e-01 2 1.333333 1.786328e-01 4 1.142857 1.184340e-02 8 1.154639 6.136312e-05 16 1.154701 1.630567e-09 32 1.154701 0.000000e+00 64 1.154701 6.661338e-16 128 1.154701 2.220446e-16 10 0.693147 1 0.666667 2.648051e-02 2 0.685714 7.432895e-03 4 0.691220 1.927289e-03 8 0.692661 4.866265e-04 16 0.693025 1.219662e-04 32 0.693117 3.051106e-05 64 0.693140 7.628987e-06 128 0.693145 1.907323e-06 11 0.379885 1 0.377541 2.344824e-03 2 0.379322 5.630931e-04 4 0.379746 1.394595e-04 8 0.379851 3.478450e-05 16 0.379877 8.691127e-06 32 0.379883 2.172470e-06 64 0.379885 5.430980e-07 128 0.379885 1.357733e-07 12 0.777505 1 0.770747 6.757593e-03 2 0.775822 1.682501e-03 4 0.777084 4.202010e-04 8 0.777400 1.050238e-04 16 0.777478 2.625431e-05 32 0.777498 6.563475e-06 64 0.777503 1.640862e-06 128 0.777504 4.102152e-07 13 1.658348 1 -1.917849 3.576196e+00 2 1.822278 1.639300e-01 4 1.682149 2.380164e-02 8 1.663648 5.300614e-03 16 1.659636 1.288876e-03 32 1.658668 3.200129e-04 64 1.658427 7.986627e-05 128 1.658368 1.995802e-05 14 0.500000 1 0.000000 5.000002e-01 2 0.000000 5.000002e-01 4 0.000000 5.000002e-01 8 0.000000 5.000002e-01 16 0.000001 4.999992e-01 32 0.047735 4.522653e-01 64 0.423773 7.622746e-02 128 0.499966 3.403412e-05 15 1.000000 1 0.000000 1.000000e+00 2 0.000000 1.000000e+00 4 0.000000 1.000000e+00 8 0.000005 9.999949e-01 16 0.006323 9.936774e-01 32 0.157218 8.427817e-01 64 0.565397 4.346025e-01 128 0.857119 1.428811e-01 16 0.499363 1 0.025424 4.739393e-01 2 0.056261 4.431029e-01 4 0.116750 3.826133e-01 8 0.225744 2.736193e-01 16 0.375544 1.238191e-01 32 0.476020 2.334311e-02 64 0.493313 6.050009e-03 128 0.493635 5.728801e-03 17 0.500000 1 0.000000 5.000000e-01 2 1.000000 5.000000e-01 4 0.500000 9.436896e-16 8 0.500000 8.881784e-16 16 0.500000 4.996004e-16 32 0.500000 1.110223e-16 64 0.500000 0.000000e+00 128 0.500000 3.330669e-16 18 0.170557 1 0.188770 1.821298e-02 2 0.175036 4.478576e-03 4 0.171673 1.115191e-03 8 0.170836 2.785227e-04 16 0.170627 6.961354e-05 32 0.170575 1.740231e-05 64 0.170562 4.350512e-06 128 0.170558 1.087624e-06 19 -1.000000 1 -0.693147 3.068528e-01 2 -0.836988 1.630118e-01 4 -0.915951 8.404855e-02 8 -0.957329 4.267125e-02 16 -0.978502 2.149813e-02 32 -0.989210 1.078974e-02 64 -0.994595 5.405040e-03 128 -0.997295 2.705063e-03 20 1.564396 1 1.990050 4.256533e-01 2 1.593625 2.922905e-02 4 1.574727 1.033024e-02 8 1.566987 2.591033e-03 16 1.565044 6.477994e-04 32 1.564558 1.619499e-04 64 1.564437 4.048743e-05 128 1.564407 1.012185e-05 21 0.210803 1 0.009866 2.009367e-01 2 0.393257 1.824545e-01 4 0.177981 3.282172e-02 8 0.199073 1.172972e-02 16 0.226581 1.577853e-02 32 0.203178 7.624375e-03 64 0.212309 1.506556e-03 128 0.209728 1.074499e-03 22 0.728103 1 0.761905 3.380185e-02 2 0.734977 6.873822e-03 4 0.729839 1.735593e-03 8 0.728537 4.340201e-04 16 0.728211 1.085068e-04 32 0.728130 2.712673e-05 64 0.728110 6.781684e-06 128 0.728105 1.695421e-06 23 0.624713 1 1.818595 1.193882e+00 2 -0.865646 1.490360e+00 4 2.943344 2.318630e+00 8 -0.265766 8.904790e-01 16 1.057193 4.324796e-01 32 3.045525 2.420812e+00 64 1.569020 9.443071e-01 128 -1.791127 2.415840e+00 24 -0.006755 1 0.112539 1.192936e-01 2 -0.034657 2.790268e-02 4 -0.028509 2.175411e-02 8 -0.017214 1.045926e-02 16 -0.005497 1.257314e-03 32 -0.006680 7.432007e-05 64 -0.006651 1.039638e-04 128 -0.006817 6.264925e-05 25 -1.610864 1 -1.609438 1.426390e-03 2 -1.897120 2.862557e-01 4 -1.502638 1.082264e-01 8 -1.674093 6.322906e-02 16 -1.581562 2.930215e-02 32 -1.626096 1.523154e-02 64 -1.603394 7.470500e-03 128 -1.614636 3.771577e-03 26 7.954927 1 2.311455 5.643472e+00 2 6.283185 1.671741e+00 4 7.920532 3.439442e-02 8 7.954925 1.251689e-06 16 7.954927 1.776357e-15 32 7.954927 4.440892e-15 64 7.954927 0.000000e+00 128 7.954927 1.776357e-15 27 0.841117 1 0.666308 1.748089e-01 2 0.724249 1.168677e-01 4 0.764438 7.667884e-02 8 0.791275 4.984213e-02 16 0.808885 3.223213e-02 32 0.820343 2.077430e-02 64 0.827762 1.335532e-02 128 0.832549 8.567423e-03 28 0.019955 1 0.000000 1.995467e-02 2 0.000000 1.995467e-02 4 0.591821 5.718663e-01 8 0.451165 4.312103e-01 16 -0.412133 4.320878e-01 32 -0.099394 1.193486e-01 64 0.076865 5.691023e-02 128 0.026009 6.054304e-03 29 0.306853 1 0.400000 9.314718e-02 2 0.000000 3.068528e-01 4 0.000000 3.068528e-01 8 0.000000 3.068528e-01 16 0.000000 3.068528e-01 32 0.000000 3.068528e-01 64 0.000000 3.068528e-01 128 0.000000 3.068528e-01 30 -4.527570 1 -5.483838 9.562683e-01 2 -18.910791 1.438322e+01 4 -15.732139 1.120457e+01 8 0.572087 5.099657e+00 16 -4.315508 2.120614e-01 32 -4.487650 3.991980e-02 64 -4.518243 9.326722e-03 128 -4.525277 2.292918e-03 31 2.651635 1 8.000000 5.348365e+00 2 1.600000 1.051635e+00 4 2.400000 2.516353e-01 8 2.642190 9.445247e-03 16 2.652188 5.521946e-04 32 2.651779 1.440119e-04 64 2.651671 3.603360e-05 128 2.651644 9.010318e-06 32 -12.070346 1 0.000000 1.207035e+01 2 -9.282786 2.787560e+00 4 -11.428302 6.420443e-01 8 -11.913846 1.565005e-01 16 -12.031480 3.886618e-02 32 -12.060646 9.700235e-03 64 -12.067922 2.424037e-03 128 -12.069740 6.059455e-04 33 0.886227 1 0.832555 5.367231e-02 2 0.856885 2.934190e-02 4 0.870846 1.538125e-02 8 0.878377 7.850219e-03 16 0.882289 3.937451e-03 32 0.884275 1.952167e-03 64 0.885267 9.603969e-04 128 0.885757 4.700697e-04 34 1085.252667 1 219.336000 8.659167e+02 2 814.086000 2.711667e+02 4 1014.043031 7.120964e+01 8 1067.236635 1.801603e+01 16 1080.735307 4.517359e+00 32 1084.122492 1.130174e+00 64 1084.970071 2.825957e-01 128 1085.182014 7.065219e-02 35 26.000000 1 16.159235 9.840765e+00 2 19.147178 6.852822e+00 4 23.973547 2.026453e+00 8 24.653718 1.346282e+00 16 24.668170 1.331830e+00 32 25.550828 4.491718e-01 64 25.063996 9.360042e-01 128 26.827707 8.277071e-01 36 100.000000 1 1.293458 9.870654e+01 2 2.600028 9.739997e+01 4 4.187874 9.581213e+01 8 6.004223 9.399578e+01 16 8.008159 9.199184e+01 32 10.165532 8.983447e+01 64 12.446581 8.755342e+01 128 14.825009 8.517499e+01 37 3.135799 1 0.011989 3.123809e+00 2 0.391087 2.744711e+00 4 0.041904 3.093895e+00 8 0.188576 2.947223e+00 16 3.406878 2.710789e-01 32 0.361297 2.774502e+00 64 1.284407 1.851392e+00 128 7.939480 4.803682e+00 38 0.539257 1 -0.457102 9.963588e-01 2 2.545267 2.006010e+00 4 -0.864262 1.403519e+00 8 0.538767 4.901286e-04 16 0.539257 3.330669e-16 32 0.539257 2.220446e-16 64 0.539257 1.110223e-16 128 0.539257 4.440892e-16 39 2.787694 1 2.449490 3.382040e-01 2 2.506647 2.810462e-01 4 2.575061 2.126331e-01 8 2.633397 1.542967e-01 16 2.677560 1.101335e-01 32 2.709557 7.813666e-02 64 2.732377 5.531630e-02 128 2.748563 3.913088e-02 40 2.698957 1 1.871865 8.270921e-01 2 3.340871 6.419141e-01 4 2.157288 5.416691e-01 8 2.446448 2.525088e-01 16 2.941221 2.422645e-01 32 2.500647 1.983097e-01 64 2.599192 9.976487e-02 128 2.943196 2.442397e-01 41 6.095585 1 1.777778 4.317807e+00 2 1.847521 4.248064e+00 4 2.015811 4.079775e+00 8 2.065591 4.029994e+00 16 1.915790 4.179795e+00 32 1.612648 4.482937e+00 64 1.262018 4.833567e+00 128 0.943020 5.152565e+00 42 3.980786 1 2.002075 1.978711e+00 2 2.368671 1.612115e+00 4 2.670305 1.310481e+00 8 2.916132 1.064654e+00 16 3.115975 8.648115e-01 32 3.278332 7.024540e-01 64 3.410215 5.705717e-01 128 3.517338 4.634486e-01 43 2.991569 1 1.292475 1.699094e+00 2 0.397806 2.593763e+00 4 0.149754 2.841815e+00 8 0.061220 2.930349e+00 16 0.026183 2.965386e+00 32 0.011523 2.980046e+00 64 0.005172 2.986397e+00 128 0.002355 2.989214e+00 44 -0.030100 1 0.000041 3.014098e-02 2 0.000476 3.057526e-02 4 -0.007115 2.298487e-02 8 -0.020678 9.421498e-03 16 -0.027361 2.739168e-03 32 -0.029387 7.126126e-04 64 -0.029920 1.799601e-04 128 -0.030055 4.510406e-05 45 -0.292707 1 -0.832294 5.395870e-01 2 0.623887 9.165941e-01 4 0.663390 9.560968e-01 8 0.500344 7.930509e-01 16 0.356408 6.491146e-01 32 0.251484 5.441910e-01 64 0.177385 4.700914e-01 128 0.125230 4.179363e-01 46 6.069091 1 4.656977 1.412114e+00 2 5.862292 2.067993e-01 4 6.065446 3.645353e-03 8 6.069090 1.095435e-06 16 6.069091 9.858780e-14 32 6.069091 1.776357e-15 64 6.069091 1.776357e-15 128 6.069091 2.664535e-15 47 -0.444444 1 -0.490129 4.568463e-02 2 -0.471144 2.669914e-02 4 -0.458076 1.363158e-02 8 -0.450859 6.414686e-03 16 -0.447304 2.859943e-03 32 -0.445672 1.227437e-03 64 -0.444957 5.121818e-04 128 -0.444654 2.091739e-04 48 -4.000000 1 -0.980258 3.019742e+00 2 -1.552388 2.447612e+00 4 -2.055125 1.944875e+00 8 -2.475353 1.524647e+00 16 -2.816794 1.183206e+00 32 -3.089153 9.108466e-01 64 -3.303505 6.964949e-01 128 -3.470439 5.295607e-01 49 52.740748 1 -11.776902 6.451765e+01 2 42.780682 9.960067e+00 4 50.480537 2.260212e+00 8 52.469150 2.715987e-01 16 51.821671 9.190769e-01 32 52.860419 1.196709e-01 64 52.796357 5.560884e-02 128 52.734623 6.125172e-03 50 -0.128137 1 -0.000000 1.281368e-01 2 -0.549306 4.211693e-01 4 0.434294 5.624305e-01 8 -0.233903 1.057661e-01 16 -0.151016 2.287922e-02 32 -0.134366 6.229426e-03 64 -0.129889 1.752596e-03 128 -0.128628 4.916281e-04 51 -0.197814 1 -0.316254 1.184406e-01 2 -0.203886 6.072261e-03 4 -0.193089 4.724765e-03 8 -0.190257 7.557041e-03 16 -0.189535 8.278957e-03 32 -0.189346 8.467852e-03 64 -0.189295 8.518571e-03 128 -0.189281 8.532598e-03 52 -0.089944 1 0.065217 1.551614e-01 2 0.909550 9.994939e-01 4 -0.931213 8.412689e-01 8 0.862596 9.525396e-01 16 -0.971462 8.815177e-01 32 0.828247 9.181910e-01 64 -0.992841 9.028972e-01 128 0.818136 9.080797e-01 53 1.504623 1 1.154701 3.499222e-01 2 2.417029 9.124061e-01 4 1.192372 3.122507e-01 8 1.296038 2.085845e-01 16 1.410330 9.429300e-02 32 1.576043 7.142020e-02 64 1.430814 7.380879e-02 128 1.473472 3.115054e-02 54 1.154701 1 1.000000 1.547005e-01 2 1.333333 1.786328e-01 4 1.142857 1.184340e-02 8 1.154639 6.136312e-05 16 1.154701 1.630567e-09 32 1.154701 2.220446e-16 64 1.154701 4.440892e-16 128 1.154701 4.440892e-16 55 0.505059 1 0.569783 6.472419e-02 2 0.552700 4.764098e-02 4 0.512356 7.296938e-03 8 0.506807 1.747918e-03 16 0.505491 4.326398e-04 32 0.505167 1.078951e-04 64 0.505086 2.695732e-05 128 0.505065 6.738303e-06 56 1.992252 1 2.222222 2.299698e-01 2 2.184300 1.920479e-01 4 2.038472 4.621965e-02 8 2.001147 8.894106e-03 16 1.994431 2.178998e-03 32 1.992794 5.419534e-04 64 1.992388 1.353154e-04 128 1.992286 3.381808e-05 57 0.400000 1 0.353553 4.644661e-02 2 0.387260 1.274047e-02 4 0.396607 3.393181e-03 8 0.399114 8.856622e-04 16 0.399772 2.280589e-04 32 0.399942 5.819148e-05 64 0.399985 1.475604e-05 128 0.399996 3.725821e-06 TEST02 Composite Simpson rule, for 1D finite interval problems. Problem Exact Ints Approx Error 1 1.718282 1 1.718861 5.793234e-04 2 1.718319 3.701346e-05 4 1.718284 2.326241e-06 8 1.718282 1.455928e-07 16 1.718282 9.102727e-09 32 1.718282 5.689700e-10 64 1.718282 3.556155e-11 128 1.718282 2.222444e-12 2 0.700000 1 0.833333 1.333333e-01 2 0.583333 1.166667e-01 4 0.708333 8.333333e-03 8 0.729167 2.916667e-02 16 0.697917 2.083333e-03 32 0.692708 7.291667e-03 64 0.700521 5.208333e-04 128 0.701823 1.822917e-03 3 0.666667 1 0.638071 2.859548e-02 2 0.656526 1.014040e-02 4 0.663079 3.587387e-03 8 0.665398 1.268478e-03 16 0.666218 4.484839e-04 32 0.666508 1.585636e-04 64 0.666611 5.606073e-05 128 0.666647 1.982046e-05 4 0.479428 1 0.479555 1.263588e-04 2 0.479555 1.268342e-04 4 0.479438 9.783843e-06 8 0.479429 6.405666e-07 16 0.479428 4.049006e-08 32 0.479428 2.537734e-09 64 0.479428 1.587195e-10 128 0.479428 9.921730e-12 5 1.582233 1 1.711367 1.291336e-01 2 1.584969 2.736293e-03 4 1.582174 5.929773e-05 8 1.582231 1.784215e-06 16 1.582233 9.284131e-08 32 1.582233 5.521886e-09 64 1.582233 3.407812e-10 128 1.582233 2.123235e-11 6 1.460447 1 1.586760 1.263125e-01 2 1.224344 2.361029e-01 4 1.440192 2.025523e-02 8 1.453274 7.172877e-03 16 1.457910 2.536831e-03 32 1.459550 8.969599e-04 64 1.460130 3.171267e-04 128 1.460335 1.121214e-04 7 2.000000 1 1.109476 8.905243e-01 2 1.370602 6.293976e-01 4 1.554972 4.450278e-01 8 1.685319 3.146806e-01 16 1.777487 2.225127e-01 32 1.842660 1.573402e-01 64 1.888744 1.112563e-01 128 1.921330 7.867010e-02 8 0.866973 1 0.877451 1.047799e-02 2 0.867114 1.407132e-04 4 0.866981 8.061650e-06 8 0.866973 5.083640e-07 16 0.866973 3.178817e-08 32 0.866973 1.986818e-09 64 0.866973 1.241764e-10 128 0.866973 7.761014e-12 9 1.154701 1 1.000000 1.547005e-01 2 1.222222 6.752168e-02 4 1.150794 3.906888e-03 8 1.154680 2.045329e-05 16 1.154701 5.435219e-10 32 1.154701 2.220446e-16 64 1.154701 6.661338e-16 128 1.154701 2.220446e-16 10 0.693147 1 0.694444 1.297264e-03 2 0.693254 1.067877e-04 4 0.693155 7.350095e-06 8 0.693148 4.722595e-07 16 0.693147 2.972988e-08 32 0.693147 1.861510e-09 64 0.693147 1.163973e-10 128 0.693147 7.275514e-12 11 0.379885 1 0.379851 3.481028e-05 2 0.379883 1.996482e-06 4 0.379885 1.223950e-07 8 0.379885 7.613688e-09 16 0.379885 4.752977e-10 32 0.379885 2.969724e-11 64 0.379885 1.855904e-12 128 0.379885 1.160183e-13 12 0.777505 1 0.777494 1.048879e-05 2 0.777504 6.460455e-07 4 0.777505 4.023384e-08 8 0.777505 2.512382e-09 16 0.777505 1.569890e-10 32 0.777505 9.811374e-12 64 0.777505 6.131762e-13 128 0.777505 3.830269e-14 13 1.658348 1 0.297431 1.360917e+00 2 1.683209 2.486096e-02 4 1.659324 9.765688e-04 8 1.658403 5.508757e-05 16 1.658351 3.358779e-06 32 1.658348 2.086393e-07 64 1.658348 1.302001e-08 128 1.658348 8.134386e-10 14 0.500000 1 11.785113 1.128511e+01 2 5.892557 5.392556e+00 4 2.946278 2.446278e+00 8 1.473139 9.731389e-01 16 0.736570 2.365700e-01 32 0.400108 9.989196e-02 64 0.474613 2.538674e-02 128 0.499989 1.148548e-05 15 1.000000 1 41.666667 4.066667e+01 2 20.833333 1.983333e+01 4 10.416667 9.416667e+00 8 5.208337 4.208337e+00 16 2.608383 1.608383e+00 32 1.407950 4.079497e-01 64 1.054703 5.470346e-02 128 1.004531 4.531435e-03 16 0.499363 1 2.670592 2.171229e+00 2 1.368566 8.692025e-01 4 0.752740 2.533762e-01 8 0.507408 8.044145e-03 16 0.466443 3.292080e-02 32 0.487977 1.138595e-02 64 0.493528 5.835797e-03 128 0.493635 5.728765e-03 17 0.500000 1 0.000000 5.000000e-01 2 0.666667 1.666667e-01 4 0.500000 6.106227e-16 8 0.500000 7.216450e-16 16 0.500000 6.106227e-16 32 0.500000 1.665335e-16 64 0.500000 0.000000e+00 128 0.500000 2.220446e-16 18 0.170557 1 0.170670 1.131103e-04 2 0.170564 6.774811e-06 4 0.170558 4.190496e-07 8 0.170557 2.612326e-08 16 0.170557 1.631656e-09 32 0.170557 1.019621e-10 64 0.170557 6.372403e-12 128 0.170557 3.982370e-13 19 -1.000000 1 -0.462098 5.379019e-01 2 -0.673517 3.264833e-01 4 -0.807895 1.921054e-01 8 -0.889508 1.104921e-01 16 -0.937534 6.246626e-02 32 -0.965157 3.484327e-02 64 -0.980773 1.922670e-02 128 -0.989484 1.051589e-02 20 1.564396 1 1.659202 9.480547e-02 2 1.560343 4.053448e-03 4 1.564385 1.140721e-05 8 1.564396 5.469474e-08 16 1.564396 8.812284e-11 32 1.564396 6.038836e-11 64 1.564396 4.631628e-12 128 1.564396 3.030909e-13 21 0.210803 1 0.018353 1.924502e-01 2 0.269703 5.890072e-02 4 0.187963 2.283987e-02 8 0.197033 1.376946e-02 16 0.216392 5.589240e-03 32 0.205885 4.918052e-03 64 0.210619 1.839260e-04 128 0.209743 1.059388e-03 22 0.728103 1 0.730159 2.055817e-03 2 0.728080 2.318515e-05 4 0.728103 1.672471e-07 8 0.728103 2.493054e-09 16 0.728103 3.848322e-11 32 0.728103 5.994094e-13 64 0.728103 9.547918e-15 128 0.728103 2.220446e-16 23 0.624713 1 1.352642 7.279285e-01 2 -0.203876 8.285891e-01 4 2.004566 1.379852e+00 8 0.334548 2.901649e-01 16 0.916364 2.916505e-01 32 2.312333 1.687620e+00 64 1.694593 1.069879e+00 128 -0.608292 1.233005e+00 24 -0.006755 1 0.101552 1.083065e-01 2 0.008914 1.566917e-02 4 -0.008772 2.017707e-03 8 -0.011111 4.356005e-03 16 -0.006351 4.034162e-04 32 -0.006713 4.170244e-05 64 -0.006677 7.777374e-05 128 -0.006775 2.020659e-05 25 -1.610864 1 -1.333067 2.777977e-01 2 -1.663040 5.217599e-02 4 -1.517092 9.377219e-02 8 -1.624169 1.330434e-02 16 -1.587444 2.342078e-02 32 -1.614192 3.327664e-03 64 -1.605009 5.855091e-03 128 -1.611696 8.319224e-04 26 7.954927 1 7.234126 7.208006e-01 2 7.420611 5.343158e-01 4 7.943463 1.146397e-02 8 7.954926 4.172296e-07 16 7.954927 8.881784e-16 32 7.954927 2.664535e-15 64 7.954927 8.881784e-16 128 7.954927 1.776357e-15 27 0.841117 1 0.527539 3.135782e-01 2 0.635551 2.055661e-01 4 0.706693 1.344243e-01 8 0.753456 8.766044e-02 16 0.784106 5.701128e-02 32 0.804134 3.698315e-02 64 0.817184 2.393274e-02 128 0.825665 1.545210e-02 28 0.019955 1 0.000000 1.995467e-02 2 0.000000 1.995467e-02 4 0.394547 3.745927e-01 8 0.399413 3.794588e-01 16 -0.150243 1.701975e-01 32 -0.072695 9.264990e-02 64 0.031461 1.150664e-02 128 0.020259 3.044861e-04 29 0.306853 1 0.350000 4.314718e-02 2 0.108333 1.985195e-01 4 0.020833 2.860195e-01 8 0.010417 2.964362e-01 16 0.005208 3.016445e-01 32 0.002604 3.042487e-01 64 0.001302 3.055507e-01 128 0.000651 3.062018e-01 30 -4.527570 1 4.131858 8.659428e+00 2 -9.627292 5.099722e+00 4 -12.149940 7.622371e+00 8 -3.071555 1.456014e+00 16 -4.508131 1.943855e-02 32 -4.526581 9.889140e-04 64 -4.527511 5.897087e-05 128 -4.527566 3.643536e-06 31 2.651635 1 5.490196 2.838561e+00 2 2.478431 1.732040e-01 4 2.572549 7.908631e-02 8 2.647735 3.900764e-03 16 2.651627 8.044380e-06 32 2.651635 4.667299e-08 64 2.651635 2.921190e-09 128 2.651635 1.826650e-10 32 -12.070346 1 -11.592840 4.775068e-01 2 -11.984944 8.540230e-02 4 -12.064209 6.137359e-03 8 -12.069951 3.949931e-04 16 -12.070321 2.486034e-05 32 -12.070345 1.556458e-06 64 -12.070346 9.732054e-08 128 -12.070346 6.083193e-09 33 0.886227 1 0.555036 3.311905e-01 2 0.710016 1.762111e-01 4 0.792758 9.346942e-02 8 0.836822 4.940465e-02 16 0.860208 2.601892e-02 32 0.872572 1.365466e-02 64 0.879085 7.142235e-03 128 0.882502 3.724431e-03 34 1085.252667 1 1168.586000 8.333333e+01 2 1090.461000 5.208333e+00 4 1085.578188 3.255208e-01 8 1085.273012 2.034505e-02 16 1085.253938 1.271566e-03 32 1085.252746 7.947286e-05 64 1085.252672 4.967054e-06 128 1085.252667 3.104410e-07 35 26.000000 1 18.645046 7.354954e+00 2 19.394102 6.605898e+00 4 22.488219 3.511781e+00 8 23.684330 2.315670e+00 16 24.178659 1.821341e+00 32 25.011853 9.881468e-01 64 24.956786 1.043214e+00 128 26.186198 1.861983e-01 36 100.000000 1 0.862306 9.913769e+01 2 1.948928 9.805107e+01 4 3.333042 9.666696e+01 8 4.971357 9.502864e+01 16 6.823747 9.317625e+01 32 8.854202 9.114580e+01 64 11.030566 8.896943e+01 128 13.324192 8.667581e+01 37 3.135799 1 0.011791 3.124008e+00 2 0.264622 2.871177e+00 4 0.095066 3.040733e+00 8 0.166266 2.969533e+00 16 2.322955 8.128433e-01 32 0.834530 2.301269e+00 64 1.213320 1.922479e+00 128 5.685579 2.549780e+00 38 0.539257 1 0.742463 2.032061e-01 2 2.144260 1.605003e+00 4 0.071744 4.675129e-01 8 0.539094 1.633762e-04 16 0.539257 3.330669e-16 32 0.539257 3.330669e-16 64 0.539257 1.110223e-16 128 0.539257 2.220446e-16 39 2.787694 1 2.125792 6.619013e-01 2 2.325746 4.619475e-01 4 2.461806 3.258881e-01 8 2.557324 2.303697e-01 16 2.624803 1.628911e-01 32 2.672513 1.151811e-01 64 2.706248 8.144528e-02 128 2.730103 5.759051e-02 40 2.698957 1 1.795749 9.032079e-01 2 2.813144 1.141875e-01 4 2.287952 4.110047e-01 8 2.415393 2.835634e-01 16 2.760769 6.181282e-02 32 2.557279 1.416775e-01 64 2.594660 1.042970e-01 128 2.826262 1.273054e-01 41 6.095585 1 1.185185 4.910400e+00 2 1.527977 4.567608e+00 4 1.651794 4.443791e+00 8 1.713029 4.382556e+00 16 1.621458 4.474127e+00 32 1.394397 4.701188e+00 64 1.110120 4.985465e+00 128 0.839016 5.256569e+00 42 3.980786 1 1.596516 2.384270e+00 2 2.043693 1.937093e+00 4 2.407271 1.573515e+00 8 2.702673 1.278114e+00 16 2.942631 1.038155e+00 32 3.137541 8.432451e-01 64 3.295858 6.849280e-01 128 3.424452 5.563345e-01 43 2.991569 1 0.861650 2.129919e+00 2 0.480616 2.510953e+00 4 0.166137 2.825432e+00 8 0.065772 2.925797e+00 16 0.027659 2.963910e+00 32 0.012046 2.979523e+00 64 0.005369 2.986200e+00 128 0.002432 2.989137e+00 44 -0.030100 1 -0.126106 9.600653e-02 2 -0.062743 3.264325e-02 4 -0.036194 6.094255e-03 8 -0.030697 5.969408e-04 16 -0.030142 4.260777e-05 32 -0.030102 2.756931e-06 64 -0.030100 1.738244e-07 128 -0.030100 1.088791e-08 45 -0.292707 1 -0.554862 2.621557e-01 2 0.277209 5.699160e-01 4 0.546241 8.389480e-01 8 0.444128 7.368345e-01 16 0.320996 6.137027e-01 32 0.227058 5.197643e-01 64 0.160170 4.528772e-01 128 0.113050 4.057572e-01 46 6.069091 1 5.741116 3.279750e-01 2 6.002590 6.650139e-02 4 6.067877 1.214387e-03 8 6.069091 3.651448e-07 16 6.069091 3.197442e-14 32 6.069091 2.664535e-15 64 6.069091 8.881784e-16 128 6.069091 8.881784e-16 47 -0.444444 1 -0.326753 1.176917e-01 2 -0.395784 4.866054e-02 4 -0.424752 1.969241e-02 8 -0.436603 7.841678e-03 16 -0.441361 3.083325e-03 32 -0.443244 1.200028e-03 64 -0.443981 4.631324e-04 128 -0.444267 1.774805e-04 48 -4.000000 1 -0.653505 3.346495e+00 2 -1.198301 2.801699e+00 4 -1.710503 2.289497e+00 8 -2.162966 1.837034e+00 16 -2.546787 1.453213e+00 32 -2.863363 1.136637e+00 64 -3.119160 8.808404e-01 128 -3.322622 6.773782e-01 49 52.740748 1 46.490980 6.249769e+00 2 53.728761 9.880130e-01 4 53.387958 6.472098e-01 8 53.259989 5.192411e-01 16 52.432917 3.078310e-01 32 52.819793 7.904463e-02 64 52.797398 5.664972e-02 128 52.755722 1.497327e-02 50 -0.128137 1 -0.000000 1.281368e-01 2 -0.366204 2.380672e-01 4 0.197978 3.261149e-01 8 -0.129329 1.191720e-03 16 -0.126358 1.779015e-03 32 -0.127587 5.497606e-04 64 -0.127992 1.447206e-04 128 -0.128100 3.670755e-05 51 -0.197814 1 -0.210836 1.302253e-02 2 -0.188633 9.180658e-03 4 -0.189061 8.752215e-03 8 -0.189187 8.626674e-03 16 -0.189240 8.573135e-03 32 -0.189262 8.551976e-03 64 -0.189270 8.543727e-03 128 -0.189273 8.540500e-03 52 -0.089944 1 -0.956205 8.662608e-01 2 0.117395 2.073386e-01 4 -0.713703 6.237589e-01 8 0.373414 4.633584e-01 16 -0.604700 5.147558e-01 32 0.411725 5.016691e-01 64 -0.594073 5.041288e-01 128 0.413861 5.038049e-01 53 1.504623 1 1.054318 4.503046e-01 2 1.946062 4.414388e-01 4 1.365107 1.395154e-01 8 1.347851 1.567722e-01 16 1.398139 1.064840e-01 32 1.514710 1.008695e-02 64 1.448557 5.606575e-02 128 1.468124 3.649844e-02 54 1.154701 1 1.000000 1.547005e-01 2 1.222222 6.752168e-02 4 1.150794 3.906888e-03 8 1.154680 2.045329e-05 16 1.154701 5.435221e-10 32 1.154701 0.000000e+00 64 1.154701 4.440892e-16 128 1.154701 4.440892e-16 55 0.505059 1 0.475874 2.918466e-02 2 0.511440 6.380958e-03 4 0.505174 1.149409e-04 8 0.505065 6.592792e-06 16 0.505059 4.032796e-07 32 0.505059 2.507072e-08 64 0.505059 1.564833e-09 128 0.505059 9.776968e-11 56 1.992252 1 1.832359 1.598937e-01 2 2.002009 9.756786e-03 4 1.995936 3.683504e-03 8 1.992320 6.788119e-05 16 1.992257 4.255033e-06 32 1.992253 2.633920e-07 64 1.992252 1.641886e-08 128 1.992252 1.025495e-09 57 0.400000 1 0.402369 2.368927e-03 2 0.400432 4.319160e-04 4 0.400077 7.724945e-05 8 0.400014 1.371347e-05 16 0.400002 2.427846e-06 32 0.400000 4.294134e-07 64 0.400000 7.592448e-08 128 0.400000 1.342257e-08 TEST03 Monte Carlo rule, for 1D finite interval problems. Problem Exact Pts Approx Error 1 1.718282 1 1.244107 4.741745e-01 2 1.923102 2.048202e-01 4 1.973010 2.547284e-01 8 1.610657 1.076253e-01 16 1.580527 1.377548e-01 32 1.617409 1.008727e-01 64 1.686509 3.177240e-02 128 1.721548 3.266253e-03 2 0.700000 1 0.000000 7.000000e-01 2 0.500000 2.000000e-01 4 0.750000 5.000000e-02 8 0.500000 2.000000e-01 16 0.562500 1.375000e-01 32 0.562500 1.375000e-01 64 0.656250 4.375000e-02 128 0.671875 2.812500e-02 3 0.666667 1 0.467352 1.993142e-01 2 0.722634 5.596701e-02 4 0.776376 1.097095e-01 8 0.605775 6.089139e-02 16 0.575543 9.112328e-02 32 0.589211 7.745559e-02 64 0.639049 2.761762e-02 128 0.657455 9.212066e-03 4 0.479428 1 0.448433 3.099490e-02 2 0.943031 4.636029e-01 4 0.607085 1.276565e-01 8 0.613233 1.338046e-01 16 0.625548 1.461195e-01 32 0.666535 1.871065e-01 64 0.551030 7.160220e-02 128 0.550946 7.151793e-02 5 1.582233 1 1.517751 6.448180e-02 2 1.170970 4.112633e-01 4 1.459975 1.222576e-01 8 1.454641 1.275919e-01 16 1.468393 1.138404e-01 32 1.419521 1.627116e-01 64 1.511977 7.025561e-02 128 1.513628 6.860483e-02 6 1.460447 1 0.502647 9.578005e-01 2 1.439867 2.058053e-02 4 1.652997 1.925503e-01 8 1.284940 1.755072e-01 16 1.401133 5.931458e-02 32 1.417813 4.263367e-02 64 1.471580 1.113271e-02 128 1.498551 3.810357e-02 7 2.000000 1 2.139713 1.397128e-01 2 1.581148 4.188517e-01 4 1.398638 6.013620e-01 8 2.002668 2.667966e-03 16 3.421430 1.421430e+00 32 3.096837 1.096837e+00 64 2.443827 4.438266e-01 128 2.178408 1.784084e-01 8 0.866973 1 0.997729 1.307563e-01 2 0.771138 9.583496e-02 4 0.782605 8.436798e-02 8 0.887123 2.014980e-02 16 0.897542 3.056891e-02 32 0.882508 1.553497e-02 64 0.870369 3.396296e-03 128 0.860328 6.644602e-03 9 1.154701 1 0.785276 3.694247e-01 2 1.373385 2.186843e-01 4 1.333989 1.792883e-01 8 1.087341 6.736000e-02 16 1.024292 1.304088e-01 32 1.069884 8.481621e-02 64 1.151444 3.256921e-03 128 1.176700 2.199897e-02 10 0.693147 1 0.820736 1.275890e-01 2 0.665950 2.719686e-02 4 0.629706 6.344092e-02 8 0.732435 3.928816e-02 16 0.743708 5.056055e-02 32 0.736067 4.291939e-02 64 0.707892 1.474526e-02 128 0.697776 4.628763e-03 11 0.379885 1 0.445611 6.572599e-02 2 0.361614 1.827171e-02 4 0.347533 3.235258e-02 8 0.397468 1.758275e-02 16 0.401275 2.138918e-02 32 0.397009 1.712347e-02 64 0.385377 5.491864e-03 128 0.380641 7.559661e-04 12 0.777505 1 0.894763 1.172586e-01 2 0.745840 3.166490e-02 4 0.719731 5.777334e-02 8 0.809459 3.195431e-02 16 0.816684 3.917921e-02 32 0.809155 3.165057e-02 64 0.787776 1.027117e-02 128 0.779222 1.716906e-03 13 1.658348 1 3.743749 2.085401e+00 2 1.799745 1.413978e-01 4 0.897335 7.610131e-01 8 2.627520 9.691721e-01 16 3.037350 1.379002e+00 32 3.060941 1.402594e+00 64 2.310675 6.523273e-01 128 2.097575 4.392270e-01 14 0.500000 1 0.000000 5.000002e-01 2 0.000000 5.000002e-01 4 0.000000 5.000002e-01 8 0.000000 5.000002e-01 16 4.190923 3.690923e+00 32 3.126150 2.626150e+00 64 1.570609 1.070608e+00 128 0.790374 2.903734e-01 15 1.000000 1 0.000000 1.000000e+00 2 0.000000 1.000000e+00 4 0.000000 1.000000e+00 8 0.000002 9.999979e-01 16 9.868101 8.868101e+00 32 6.388069 5.388069e+00 64 3.239427 2.239427e+00 128 1.656468 6.564676e-01 16 0.499363 1 0.132335 3.670280e-01 2 0.069647 4.297167e-01 4 0.042173 4.571903e-01 8 0.268092 2.312709e-01 16 1.393108 8.937446e-01 32 1.532560 1.033196e+00 64 0.964280 4.649169e-01 128 0.748219 2.488552e-01 17 0.500000 1 0.060469 4.395307e-01 2 0.179682 3.203177e-01 4 0.355675 1.443254e-01 8 0.460567 3.943269e-02 16 0.410976 8.902366e-02 32 0.455192 4.480758e-02 64 0.425232 7.476777e-02 128 0.471015 2.898542e-02 18 0.170557 1 0.097330 7.322765e-02 2 0.181409 1.085207e-02 4 0.204691 3.413364e-02 8 0.147516 2.304162e-02 16 0.142320 2.823704e-02 32 0.146237 2.432082e-02 64 0.162340 8.217218e-03 128 0.167832 2.724991e-03 19 -1.000000 1 -1.521343 5.213433e-01 2 -0.783004 2.169958e-01 4 -0.582431 4.175687e-01 8 -1.186108 1.861083e-01 16 -1.523535 5.235354e-01 32 -1.456741 4.567410e-01 64 -1.180583 1.805825e-01 128 -1.081476 8.147601e-02 20 1.564396 1 1.512684 5.171223e-02 2 1.300440 2.639560e-01 4 1.487698 7.669858e-02 8 1.484447 7.994959e-02 16 1.493140 7.125599e-02 32 1.460965 1.034310e-01 64 1.519092 4.530438e-02 128 1.520168 4.422795e-02 21 0.210803 1 0.966829 7.560266e-01 2 0.483415 2.726125e-01 4 0.242432 3.162893e-02 8 0.313597 1.027946e-01 16 0.251835 4.103249e-02 32 0.231460 2.065696e-02 64 0.219722 8.919159e-03 128 0.207244 3.558774e-03 22 0.728103 1 0.952397 2.242939e-01 2 0.657955 7.014795e-02 4 0.621308 1.067945e-01 8 0.779311 5.120807e-02 16 0.783354 5.525103e-02 32 0.767794 3.969067e-02 64 0.738241 1.013824e-02 128 0.724301 3.801754e-03 23 0.624713 1 -4.537317 5.162030e+00 2 -1.816265 2.440978e+00 4 -0.191285 8.159981e-01 8 1.188954 5.642406e-01 16 -15.696364 1.632108e+01 32 -5.869774 6.494487e+00 64 -3.216027 3.840740e+00 128 -0.557993 1.182706e+00 24 -0.006755 1 -0.071290 6.453572e-02 2 -0.043456 3.670162e-02 4 0.001379 8.133897e-03 8 0.004937 1.169158e-02 16 0.011572 1.832625e-02 32 -0.002103 4.651671e-03 64 -0.008792 2.036958e-03 128 -0.016544 9.789279e-03 25 -1.610864 1 -0.730679 8.801849e-01 2 -1.046009 5.648556e-01 4 -1.528579 8.228489e-02 8 -1.146201 4.646636e-01 16 -1.309129 3.017349e-01 32 -1.341295 2.695690e-01 64 -1.538544 7.232027e-02 128 -1.575071 3.579315e-02 26 7.954927 1 7.652337 3.025897e-01 2 12.052172 4.097245e+00 4 9.184568 1.229641e+00 8 9.331242 1.376316e+00 16 9.210327 1.255401e+00 32 9.641741 1.686815e+00 64 8.633184 6.782574e-01 128 8.616163 6.612362e-01 27 0.841117 1 0.934944 9.382663e-02 2 0.722166 1.189507e-01 4 0.654967 1.861502e-01 8 0.869820 2.870274e-02 16 1.217472 3.763548e-01 32 1.146366 3.052493e-01 64 0.966200 1.250836e-01 128 0.895813 5.469641e-02 28 0.019955 1 -0.759317 7.792720e-01 2 -0.386726 4.066810e-01 4 -0.168655 1.886096e-01 8 0.242855 2.229003e-01 16 0.752815 7.328605e-01 32 0.242770 2.228155e-01 64 0.128926 1.089713e-01 128 0.009920 1.003505e-02 29 0.306853 1 0.450772 1.439188e-01 2 0.000000 3.068528e-01 4 0.000000 3.068528e-01 8 0.000000 3.068528e-01 16 0.000000 3.068528e-01 32 0.000000 3.068528e-01 64 0.000000 3.068528e-01 128 0.000000 3.068528e-01 30 -4.527570 1 -35.185606 3.065804e+01 2 -16.070870 1.154330e+01 4 -12.688981 8.161411e+00 8 -12.162205 7.634635e+00 16 -12.148689 7.621120e+00 32 -16.089435 1.156187e+01 64 -11.960709 7.433140e+00 128 -8.124779 3.597209e+00 31 2.651635 1 1.316992 1.334643e+00 2 0.937700 1.713935e+00 4 2.328685 3.229500e-01 8 2.229524 4.221118e-01 16 2.359742 2.918929e-01 32 2.005098 6.465374e-01 64 2.267436 3.841995e-01 128 2.295643 3.559923e-01 32 -12.070346 1 4.827375 1.689772e+01 2 -28.976549 1.690620e+01 4 -24.519687 1.244934e+01 8 -10.275557 1.794790e+00 16 -8.172891 3.897455e+00 32 -10.378087 1.692260e+00 64 -11.526608 5.437385e-01 128 -13.031200 9.608539e-01 33 0.886227 1 1.233427 3.472005e-01 2 0.722384 1.638425e-01 4 0.659146 2.270811e-01 8 0.984075 9.784764e-02 16 1.084434 1.982074e-01 32 1.052915 1.666880e-01 64 0.951162 6.493462e-02 128 0.908234 2.200678e-02 34 1085.252667 1 1.117222 1.084135e+03 2 2504.686114 1.419433e+03 4 2003.022123 9.177695e+02 8 1012.166013 7.308665e+01 16 803.441463 2.818112e+02 32 955.438427 1.298142e+02 64 1017.248065 6.800460e+01 128 1136.925210 5.167254e+01 35 26.000000 1 28.325934 2.325934e+00 2 19.747540 6.252460e+00 4 16.664546 9.335454e+00 8 31.775114 5.775114e+00 16 30.698675 4.698675e+00 32 29.759931 3.759931e+00 64 26.967834 9.678344e-01 128 24.702650 1.297350e+00 36 100.000000 1 5.982285 9.401771e+01 2 3.014391 9.698561e+01 4 1.804819 9.819518e+01 8 7.645725 9.235427e+01 16 123.599863 2.359986e+01 32 82.736585 1.726341e+01 64 45.567902 5.443210e+01 128 28.057012 7.194299e+01 37 3.135799 1 0.003038 3.132761e+00 2 0.018233 3.117566e+00 4 0.139405 2.996394e+00 8 0.071535 3.064263e+00 16 0.533229 2.602570e+00 32 0.313135 2.822664e+00 64 0.558874 2.576925e+00 128 0.596582 2.539216e+00 38 0.539257 1 1.095846 5.565891e-01 2 1.268236 7.289787e-01 4 0.174725 3.645321e-01 8 0.098784 4.404724e-01 16 0.638181 9.892408e-02 32 0.301967 2.372900e-01 64 0.395092 1.441652e-01 128 0.418528 1.207289e-01 39 2.787694 1 2.949929 1.622353e-01 2 2.108442 6.792513e-01 4 1.932287 8.554072e-01 8 2.363178 4.245158e-01 16 2.251327 5.363670e-01 32 2.471234 3.164600e-01 64 2.472249 3.154447e-01 128 2.442141 3.455525e-01 40 2.698957 1 1.328055 1.370901e+00 2 1.873440 8.255168e-01 4 2.655619 4.333765e-02 8 2.004821 6.941357e-01 16 2.518136 1.808209e-01 32 2.384148 3.148083e-01 64 2.696541 2.415789e-03 128 2.717379 1.842203e-02 41 6.095585 1 4.307827 1.787758e+00 2 2.153914 3.941671e+00 4 1.076957 5.018628e+00 8 0.538478 5.557107e+00 16 0.269239 5.826346e+00 32 0.134620 5.960966e+00 64 0.067310 6.028275e+00 128 0.033655 6.061930e+00 42 3.980786 1 3.367607 6.131794e-01 2 2.470498 1.510288e+00 4 2.108647 1.872139e+00 8 3.343027 6.377592e-01 16 9.288715 5.307928e+00 32 7.675779 3.694992e+00 64 5.354005 1.373219e+00 128 4.352783 3.719968e-01 43 2.991569 1 0.745489 2.246080e+00 2 0.372744 2.618825e+00 4 0.186372 2.805197e+00 8 0.093186 2.898383e+00 16 0.046593 2.944976e+00 32 0.023297 2.968272e+00 64 0.011648 2.979921e+00 128 0.005824 2.985745e+00 44 -0.030100 1 0.000000 3.009983e-02 2 -0.131833 1.017334e-01 4 -0.067336 3.723664e-02 8 -0.033667 3.567393e-03 16 -0.016803 1.329624e-02 32 -0.013723 1.637707e-02 64 -0.012064 1.803544e-02 128 -0.024378 5.721887e-03 45 -0.292707 1 1.553865 1.846572e+00 2 0.776932 1.069639e+00 4 0.388466 6.811729e-01 8 0.194233 4.869398e-01 16 0.097117 3.898233e-01 32 0.048558 3.412650e-01 64 0.024279 3.169858e-01 128 0.012140 3.048463e-01 46 6.069091 1 6.177479 1.083883e-01 2 6.992414 9.233230e-01 4 6.351491 2.824002e-01 8 6.374301 3.052103e-01 16 6.326096 2.570050e-01 32 6.439305 3.702138e-01 64 6.229605 1.605145e-01 128 6.224596 1.555048e-01 47 -0.444444 1 -0.711003 2.665590e-01 2 -0.377341 6.710331e-02 4 -0.339303 1.051414e-01 8 -0.505305 6.086084e-02 16 -0.473959 2.951461e-02 32 -0.459880 1.543537e-02 64 -0.443739 7.052935e-04 128 -0.434112 1.033207e-02 48 -4.000000 1 -3.255238 7.447623e-01 2 -1.650456 2.349544e+00 4 -1.068939 2.931061e+00 8 -3.191669 8.083308e-01 16 -12.648365 8.648365e+00 32 -10.200923 6.200923e+00 64 -6.437260 2.437260e+00 128 -4.823038 8.230383e-01 49 52.740748 1 -0.092429 5.283318e+01 2 134.832939 8.209219e+01 4 104.582389 5.184164e+01 8 51.187916 1.552832e+00 16 39.038793 1.370196e+01 32 48.386681 4.354067e+00 64 50.973853 1.766896e+00 128 57.173146 4.432398e+00 50 -0.128137 1 -0.831986 7.038488e-01 2 -0.394099 2.659618e-01 4 -0.099852 2.828440e-02 8 -0.477515 3.493782e-01 16 -0.674316 5.461788e-01 32 -0.378319 2.501822e-01 64 -0.199560 7.142296e-02 128 -0.124855 3.282324e-03 51 -0.197814 1 -0.138483 5.933102e-02 2 -0.091485 1.063285e-01 4 -0.170561 2.725291e-02 8 -0.154114 4.369990e-02 16 -0.164259 3.355492e-02 32 -0.154954 4.285976e-02 64 -0.176959 2.085437e-02 128 -0.177520 2.029400e-02 52 -0.089944 1 3.142119 3.232063e+00 2 1.572237 1.662181e+00 4 0.796015 8.859594e-01 8 -0.011325 7.861919e-02 16 -0.561527 4.715829e-01 32 -0.674917 5.849725e-01 64 -0.141860 5.191582e-02 128 -0.449534 3.595900e-01 53 1.504623 1 0.812322 6.923008e-01 2 0.955918 5.487052e-01 4 1.236042 2.685810e-01 8 1.033748 4.708748e-01 16 1.240878 2.637448e-01 32 1.202262 3.023610e-01 64 1.409583 9.503941e-02 128 1.439437 6.518549e-02 54 1.154701 1 0.785276 3.694247e-01 2 1.373385 2.186843e-01 4 1.333989 1.792883e-01 8 1.087341 6.736000e-02 16 1.024292 1.304088e-01 32 1.069884 8.481621e-02 64 1.151444 3.256921e-03 128 1.176700 2.199897e-02 55 0.505059 1 0.078613 4.264451e-01 2 0.380178 1.248804e-01 4 0.607958 1.028994e-01 8 0.368676 1.363831e-01 16 0.414094 9.096513e-02 32 0.422504 8.255452e-02 64 0.493449 1.160979e-02 128 0.507399 2.340757e-03 56 1.992252 1 2.146150 1.538979e-01 2 1.749753 2.424991e-01 4 1.939637 5.261550e-02 8 1.931966 6.028669e-02 16 1.894770 9.748201e-02 32 1.891518 1.007341e-01 64 1.964672 2.758031e-02 128 1.962885 2.936739e-02 57 0.400000 1 0.102078 2.979217e-01 2 0.518638 1.186378e-01 4 0.553435 1.534353e-01 8 0.333197 6.680349e-02 16 0.319879 8.012056e-02 32 0.342199 5.780117e-02 64 0.382877 1.712252e-02 128 0.403507 3.507465e-03 TEST04 Use a composite 4 point Gauss-Legendre rule, for 1D finite interval problems. Problem Exact Ints Approx Error 1 1.718282 1 1.718282 9.329675e-10 2 1.718282 3.741674e-12 4 1.718282 1.465494e-14 8 1.718282 2.220446e-16 16 1.718282 4.440892e-16 32 1.718282 0.000000e+00 64 1.718282 2.220446e-16 128 1.718282 2.220446e-16 2 0.700000 1 0.826073 1.260726e-01 2 0.750000 5.000000e-02 4 0.706518 6.518144e-03 8 0.687500 1.250000e-02 16 0.698370 1.629536e-03 32 0.703125 3.125000e-03 64 0.700407 4.073840e-04 128 0.699219 7.812500e-04 3 0.666667 1 0.667828 1.160979e-03 2 0.667077 4.104740e-04 4 0.666812 1.451245e-04 8 0.666718 5.130926e-05 16 0.666685 1.814056e-05 32 0.666673 6.413658e-06 64 0.666669 2.267570e-06 128 0.666667 8.017072e-07 4 0.479428 1 0.479428 9.399092e-09 2 0.479428 1.930693e-10 4 0.479428 9.782730e-13 8 0.479428 3.941292e-15 16 0.479428 5.551115e-17 32 0.479428 5.551115e-17 64 0.479428 0.000000e+00 128 0.479428 5.551115e-17 5 1.582233 1 1.585060 2.827524e-03 2 1.582214 1.930856e-05 4 1.582233 3.656264e-08 8 1.582233 3.304690e-11 16 1.582233 1.458833e-13 32 1.582233 2.220446e-16 64 1.582233 2.220446e-16 128 1.582233 8.881784e-16 6 1.460447 1 1.473444 1.299700e-02 2 1.486176 2.572910e-02 4 1.461268 8.209420e-04 8 1.460737 2.902490e-04 16 1.460550 1.026185e-04 32 1.460483 3.628113e-05 64 1.460460 1.282732e-05 128 1.460452 4.535141e-06 7 2.000000 1 1.806343 1.936575e-01 2 1.863063 1.369366e-01 4 1.903171 9.682882e-02 8 1.931532 6.846832e-02 16 1.951586 4.841441e-02 32 1.965766 3.423416e-02 64 1.975793 2.420721e-02 128 1.982883 1.711708e-02 8 0.866973 1 0.866956 1.732989e-05 2 0.866973 5.613566e-08 4 0.866973 1.679805e-10 8 0.866973 5.585532e-13 16 0.866973 1.998401e-15 32 0.866973 1.110223e-16 64 0.866973 0.000000e+00 128 0.866973 2.220446e-16 9 1.154701 1 1.197813 4.311276e-02 2 1.246607 9.190634e-02 4 1.147746 6.954610e-03 8 1.154665 3.574995e-05 16 1.154701 9.499237e-10 32 1.154701 0.000000e+00 64 1.154701 0.000000e+00 128 1.154701 2.220446e-16 10 0.693147 1 0.693146 7.631145e-07 2 0.693147 6.806386e-09 4 0.693147 3.723388e-11 8 0.693147 1.619815e-13 16 0.693147 6.661338e-16 32 0.693147 1.110223e-16 64 0.693147 1.110223e-16 128 0.693147 1.110223e-16 11 0.379885 1 0.379885 1.272926e-09 2 0.379885 3.834044e-12 4 0.379885 1.421085e-14 8 0.379885 5.551115e-17 16 0.379885 0.000000e+00 32 0.379885 0.000000e+00 64 0.379885 0.000000e+00 128 0.379885 5.551115e-17 12 0.777505 1 0.777505 1.361589e-11 2 0.777505 5.062617e-14 4 0.777505 0.000000e+00 8 0.777505 2.220446e-16 16 0.777505 1.110223e-16 32 0.777505 2.220446e-16 64 0.777505 2.220446e-16 128 0.777505 1.110223e-16 13 1.658348 1 1.666102 7.754171e-03 2 1.658338 9.470520e-06 4 1.658348 2.657638e-08 8 1.658348 9.438494e-11 16 1.658348 3.601563e-13 32 1.658348 1.110223e-15 64 1.658348 8.881784e-16 128 1.658348 6.661338e-16 14 0.500000 1 0.000000 5.000002e-01 2 0.000000 5.000002e-01 4 0.027063 4.729377e-01 8 0.470876 2.912388e-02 16 0.573638 7.363784e-02 32 0.493226 6.774462e-03 64 0.500077 7.697052e-05 128 0.500000 1.750487e-07 15 1.000000 1 0.000001 9.999987e-01 2 0.003699 9.963013e-01 4 0.141785 8.582146e-01 8 0.621078 3.789216e-01 16 0.947909 5.209059e-02 32 0.998223 1.776979e-03 64 0.999981 1.893131e-05 128 1.000000 1.045036e-07 16 0.499363 1 0.236976 2.623876e-01 2 0.400596 9.876721e-02 4 0.509088 9.724324e-03 8 0.503719 4.356079e-03 16 0.493170 6.193424e-03 32 0.493618 5.745772e-03 64 0.493635 5.728400e-03 128 0.493635 5.728730e-03 17 0.500000 1 0.997235 4.972353e-01 2 0.515987 1.598715e-02 4 0.500000 1.110223e-15 8 0.500000 5.551115e-16 16 0.500000 3.885781e-16 32 0.500000 0.000000e+00 64 0.500000 0.000000e+00 128 0.500000 5.551115e-17 18 0.170557 1 0.170557 6.749800e-10 2 0.170557 3.126416e-12 4 0.170557 1.221245e-14 8 0.170557 5.551115e-17 16 0.170557 0.000000e+00 32 0.170557 2.775558e-17 64 0.170557 2.775558e-17 128 0.170557 0.000000e+00 19 -1.000000 1 -0.968536 3.146402e-02 2 -0.984268 1.573208e-02 4 -0.992134 7.866040e-03 8 -0.996067 3.933020e-03 16 -0.998033 1.966510e-03 32 -0.999017 9.832550e-04 64 -0.999508 4.916275e-04 128 -0.999754 2.458138e-04 20 1.564396 1 1.562267 2.129295e-03 2 1.564406 9.493715e-06 4 1.564396 2.224436e-08 8 1.564396 2.915446e-13 16 1.564396 0.000000e+00 32 1.564396 0.000000e+00 64 1.564396 2.220446e-16 128 1.564396 4.440892e-16 21 0.210803 1 0.128374 8.242829e-02 2 0.197150 1.365300e-02 4 0.197678 1.312482e-02 8 0.197680 1.312242e-02 16 0.210842 3.899553e-05 32 0.209812 9.902591e-04 64 0.209975 8.272468e-04 128 0.210004 7.990218e-04 22 0.728103 1 0.728090 1.339604e-05 2 0.728103 3.911765e-08 4 0.728103 2.125433e-11 8 0.728103 8.337775e-14 16 0.728103 3.330669e-16 32 0.728103 2.220446e-16 64 0.728103 0.000000e+00 128 0.728103 0.000000e+00 23 0.624713 1 3.176652 2.551939e+00 2 -0.594889 1.219602e+00 4 2.252750 1.628037e+00 8 1.844057 1.219344e+00 16 -3.188560 3.813273e+00 32 2.454704 1.829990e+00 64 -2.144914 2.769627e+00 128 1.291870 6.671572e-01 24 -0.006755 1 0.003636 1.039025e-02 2 0.015256 2.201075e-02 4 0.004790 1.154427e-02 8 -0.005612 1.142808e-03 16 -0.006593 1.614954e-04 32 -0.006517 2.381636e-04 64 -0.006789 3.386972e-05 128 -0.006731 2.394902e-05 25 -1.610864 1 -1.802888 1.920235e-01 2 -1.572787 3.807739e-02 4 -1.565758 4.510661e-02 8 -1.601345 9.519597e-03 16 -1.599588 1.127666e-02 32 -1.608484 2.379899e-03 64 -1.608045 2.819164e-03 128 -1.610269 5.949748e-04 26 7.954927 1 7.940916 1.401019e-02 2 7.952632 2.294098e-03 4 7.954963 3.657153e-05 8 7.954927 1.336596e-09 16 7.954927 8.881784e-16 32 7.954927 1.776357e-15 64 7.954927 1.776357e-15 128 7.954927 8.881784e-16 27 0.841117 1 0.797664 4.345318e-02 2 0.813100 2.801699e-02 4 0.823093 1.802367e-02 8 0.829546 1.157076e-02 16 0.833703 7.413970e-03 32 0.836375 4.742218e-03 64 0.838088 3.028460e-03 128 0.839186 1.931240e-03 28 0.019955 1 0.124191 1.042363e-01 2 -0.177256 1.972103e-01 4 0.094897 7.494280e-02 8 0.227422 2.074670e-01 16 0.354106 3.341510e-01 32 0.022545 2.590463e-03 64 0.019942 1.230371e-05 128 0.019955 1.838019e-08 29 0.306853 1 0.346116 3.926290e-02 2 0.213531 9.332177e-02 4 0.000000 3.068528e-01 8 0.000000 3.068528e-01 16 0.000000 3.068528e-01 32 0.000000 3.068528e-01 64 0.000000 3.068528e-01 128 0.000000 3.068528e-01 30 -4.527570 1 -23.102350 1.857478e+01 2 1.533015 6.060584e+00 4 -4.105014 4.225552e-01 8 -4.530446 2.876188e-03 16 -4.527572 2.131468e-06 32 -4.527570 6.586660e-09 64 -4.527570 2.436096e-11 128 -4.527570 7.549517e-14 31 2.651635 1 2.047285 6.043503e-01 2 2.655426 3.791118e-03 4 2.650818 8.175622e-04 8 2.651645 9.804786e-06 16 2.651635 2.338863e-08 32 2.651635 8.215650e-14 64 2.651635 4.440892e-16 128 2.651635 1.332268e-15 32 -12.070346 1 -12.070189 1.568261e-04 2 -12.070343 3.238376e-06 4 -12.070346 1.501408e-08 8 -12.070346 6.075673e-11 16 -12.070346 2.451372e-13 32 -12.070346 5.329071e-15 64 -12.070346 5.329071e-15 128 -12.070346 3.552714e-15 33 0.886227 1 0.880399 5.827988e-03 2 0.883352 2.874553e-03 4 0.884818 1.408884e-03 8 0.885539 6.876771e-04 16 0.885892 3.348057e-04 32 0.886064 1.627788e-04 64 0.886148 7.909524e-05 128 0.886188 3.843201e-05 34 1085.252667 1 1085.252667 4.547474e-13 2 1085.252667 0.000000e+00 4 1085.252667 0.000000e+00 8 1085.252667 0.000000e+00 16 1085.252667 0.000000e+00 32 1085.252667 2.273737e-13 64 1085.252667 2.273737e-13 128 1085.252667 2.273737e-13 35 26.000000 1 29.100212 3.100212e+00 2 21.443668 4.556332e+00 4 121.740220 9.574022e+01 8 32.250500 6.250500e+00 16 30.684954 4.684954e+00 32 26.543024 5.430245e-01 64 25.849849 1.501511e-01 128 25.451798 5.482018e-01 36 100.000000 1 6.298537 9.370146e+01 2 8.341271 9.165873e+01 4 10.530627 8.946937e+01 8 12.837804 8.716220e+01 16 15.237205 8.476280e+01 32 17.706130 8.229387e+01 64 20.224507 7.977549e+01 128 22.774642 7.722536e+01 37 3.135799 1 0.033832 3.101966e+00 2 0.081837 3.053961e+00 4 0.197291 2.938508e+00 8 1.212995 1.922804e+00 16 0.643995 2.491804e+00 32 1.645182 1.490617e+00 64 3.237779 1.019802e-01 128 2.598738 5.370609e-01 38 0.539257 1 1.513047 9.737903e-01 2 0.406660 1.325971e-01 4 0.540695 1.437627e-03 8 0.539257 5.233767e-07 16 0.539257 9.992007e-16 32 0.539257 4.440892e-16 64 0.539257 3.330669e-16 128 0.539257 1.110223e-16 39 2.787694 1 6.781396 3.993703e+00 2 5.611634 2.823940e+00 4 4.784520 1.996826e+00 8 4.199663 1.411969e+00 16 3.786107 9.984131e-01 32 3.493678 7.059847e-01 64 3.286900 4.992066e-01 128 3.140686 3.529923e-01 40 2.698957 1 2.105072 5.938846e-01 2 2.284680 4.142764e-01 4 2.417203 2.817531e-01 8 2.651521 4.743571e-02 16 2.548058 1.508984e-01 32 2.605726 9.323083e-02 64 2.656170 4.278673e-02 128 2.637612 6.134424e-02 41 6.095585 1 4.294417 1.801168e+00 2 4.008307 2.087278e+00 4 3.755146 2.340439e+00 8 3.326836 2.768749e+00 16 2.779464 3.316121e+00 32 2.198842 3.896743e+00 64 1.665224 4.430361e+00 128 1.224032 4.871553e+00 42 3.980786 1 2.967363 1.013423e+00 2 3.157645 8.231416e-01 4 3.312190 6.685959e-01 8 3.437718 5.430681e-01 16 3.539678 4.411082e-01 32 3.622495 3.582912e-01 64 3.689763 2.910229e-01 128 3.744402 2.363840e-01 43 2.991569 1 2.107109 8.844601e-01 2 0.403218 2.588351e+00 4 0.146999 2.844570e+00 8 0.059711 2.931858e+00 16 0.025519 2.966050e+00 32 0.011241 2.980328e+00 64 0.005052 2.986517e+00 128 0.002304 2.989265e+00 44 -0.030100 1 -0.023600 6.499705e-03 2 -0.029706 3.936359e-04 4 -0.030094 5.594865e-06 8 -0.030100 3.338153e-08 16 -0.030100 1.454571e-10 32 -0.030100 5.837379e-13 64 -0.030100 2.307182e-15 128 -0.030100 2.428613e-17 45 -0.292707 1 -0.362859 7.015220e-02 2 0.846580 1.139287e+00 4 0.845025 1.137732e+00 8 0.635979 9.286854e-01 16 0.453767 7.464742e-01 32 0.320632 6.133388e-01 64 0.226351 5.190581e-01 128 0.159874 4.525804e-01 46 6.069091 1 6.063372 5.718707e-03 2 6.068904 1.873716e-04 4 6.069095 3.756318e-06 8 6.069091 1.169730e-09 16 6.069091 0.000000e+00 32 6.069091 1.776357e-15 64 6.069091 8.881784e-16 128 6.069091 3.552714e-15 47 -0.444444 1 -0.448878 4.433110e-03 2 -0.446296 1.851869e-03 4 -0.445200 7.553274e-04 8 -0.444747 3.026134e-04 16 -0.444564 1.195641e-04 32 -0.444491 4.671790e-05 64 -0.444463 1.808903e-05 128 -0.444451 6.951139e-06 48 -4.000000 1 -2.562461 1.437539e+00 2 -2.888589 1.111411e+00 4 -3.146997 8.530032e-01 8 -3.349377 6.506229e-01 16 -3.506382 4.936182e-01 32 -3.627230 3.727701e-01 64 -3.719633 2.803674e-01 128 -3.789886 2.101144e-01 49 52.740748 1 52.491094 2.496542e-01 2 50.737008 2.003740e+00 4 52.243512 4.972363e-01 8 52.562081 1.786675e-01 16 52.686142 5.460643e-02 32 52.631350 1.093981e-01 64 52.723150 1.759871e-02 128 52.683296 5.745266e-02 50 -0.128137 1 -0.183037 5.490005e-02 2 0.067921 1.960582e-01 4 -0.131315 3.178502e-03 8 -0.128444 3.072448e-04 16 -0.128216 7.906152e-05 32 -0.128157 1.987879e-05 64 -0.128142 4.976910e-06 128 -0.128138 1.244682e-06 51 -0.197814 1 -0.189169 8.644413e-03 2 -0.189298 8.516031e-03 4 -0.189284 8.529942e-03 8 -0.189278 8.535167e-03 16 -0.189276 8.537159e-03 32 -0.189276 8.537911e-03 64 -0.189275 8.538195e-03 128 -0.189275 8.538303e-03 52 -0.089944 1 -0.165815 7.587119e-02 2 -16.434964 1.634502e+01 4 16.283211 1.637316e+01 8 -16.453589 1.636365e+01 16 16.275779 1.636572e+01 32 -16.455404 1.636546e+01 64 16.275533 1.636548e+01 128 -16.455420 1.636548e+01 53 1.504623 1 1.335150 1.694728e-01 2 1.244343 2.602794e-01 4 2.138385 6.337627e-01 8 1.396267 1.083562e-01 16 1.495503 9.119613e-03 32 1.450471 5.415201e-02 64 1.465288 3.933484e-02 128 1.512136 7.513112e-03 54 1.154701 1 1.197813 4.311276e-02 2 1.246607 9.190634e-02 4 1.147746 6.954610e-03 8 1.154665 3.574995e-05 16 1.154701 9.499239e-10 32 1.154701 2.220446e-16 64 1.154701 2.220446e-16 128 1.154701 4.440892e-16 55 0.505059 1 0.506864 1.805343e-03 2 0.505046 1.258923e-05 4 0.505059 1.341399e-09 8 0.505059 8.353762e-12 16 0.505059 3.363976e-14 32 0.505059 2.220446e-16 64 0.505059 1.110223e-16 128 0.505059 0.000000e+00 56 1.992252 1 1.978705 1.354784e-02 2 1.993020 7.673128e-04 4 1.992244 8.577808e-06 8 1.992252 8.746735e-09 16 1.992252 1.028555e-11 32 1.992252 2.864375e-14 64 1.992252 0.000000e+00 128 1.992252 2.220446e-16 57 0.400000 1 0.399950 4.961499e-05 2 0.399991 8.771771e-06 4 0.399998 1.550651e-06 8 0.400000 2.741190e-07 16 0.400000 4.845785e-08 32 0.400000 8.566219e-09 64 0.400000 1.514308e-09 128 0.400000 2.676945e-10 TEST05 Composite trapezoid rule, for 1D finite interval problems. Problem Exact Ints Approx Error 1 1.718282 4 1.727222 8.940076e-03 8 1.720519 2.236764e-03 16 1.718841 5.593001e-04 32 1.718422 1.398319e-04 64 1.718317 3.495839e-05 128 1.718291 8.739624e-06 2 0.700000 4 0.625000 7.500000e-02 8 0.687500 1.250000e-02 16 0.718750 1.875000e-02 32 0.703125 3.125000e-03 64 0.695312 4.687500e-03 128 0.699219 7.812500e-04 3 0.666667 4 0.643283 2.338362e-02 8 0.658130 8.536445e-03 16 0.663581 3.085470e-03 32 0.665559 1.107730e-03 64 0.666271 3.958553e-04 128 0.666526 1.410094e-04 4 0.479428 4 0.559499 8.007104e-02 8 0.499453 2.002510e-02 16 0.484435 5.006755e-03 32 0.480680 1.251719e-03 64 0.479741 3.129317e-04 128 0.479506 7.823304e-05 5 1.582233 4 1.552712 2.952135e-02 8 1.574808 7.424810e-03 16 1.580375 1.857541e-03 32 1.581769 4.644548e-04 64 1.582117 1.161178e-04 128 1.582204 2.902972e-05 6 1.460447 4 1.336516 1.239308e-01 8 1.414273 4.617413e-02 16 1.443524 1.692319e-02 32 1.454314 6.133421e-03 64 1.458241 2.206075e-03 128 1.459658 7.893638e-04 7 2.000000 4 1.267229 7.327715e-01 8 1.483036 5.169637e-01 16 1.634749 3.652513e-01 32 1.741803 2.581973e-01 64 1.817446 1.825545e-01 128 1.870919 1.290809e-01 8 0.866973 4 0.861732 5.240653e-03 8 0.865669 1.304117e-03 16 0.866647 3.256480e-04 32 0.866892 8.138816e-05 64 0.866953 2.034555e-05 128 0.866968 5.086294e-06 9 1.154701 4 1.166667 1.196613e-02 8 1.154762 6.136638e-05 16 1.154701 1.630567e-09 32 1.154701 4.440892e-16 64 1.154701 4.440892e-16 128 1.154701 0.000000e+00 10 0.693147 4 0.697024 3.876629e-03 8 0.694122 9.746698e-04 16 0.693391 2.440216e-04 32 0.693208 6.102771e-05 64 0.693162 1.525832e-05 128 0.693151 3.814668e-06 11 0.379885 4 0.380164 2.785518e-04 8 0.379955 6.954616e-05 16 0.379903 1.738083e-05 32 0.379890 4.344851e-06 64 0.379887 1.086190e-06 128 0.379886 2.715462e-07 12 0.777505 4 0.778345 8.402813e-04 8 0.777715 2.100401e-04 16 0.777557 5.250815e-05 32 0.777518 1.312692e-05 64 0.777508 3.281723e-06 128 0.777505 8.204302e-07 13 1.658348 4 1.613674 4.467357e-02 8 1.647912 1.043597e-02 16 1.655780 2.567676e-03 32 1.657708 6.393998e-04 64 1.658188 1.596935e-04 128 1.658308 3.991360e-05 14 0.500000 4 8.838835 8.338835e+00 8 4.419417 3.919417e+00 16 2.209709 1.709708e+00 32 1.104855 6.048546e-01 64 0.576295 7.629468e-02 128 0.500034 3.361179e-05 15 1.000000 4 31.250000 3.025000e+01 8 15.625000 1.462500e+01 16 7.812503 6.812503e+00 32 3.909413 2.909413e+00 64 2.033315 1.033315e+00 128 1.299356 2.993564e-01 16 0.499363 4 2.024719 1.525355e+00 8 1.070734 5.713709e-01 16 0.648239 1.488758e-01 32 0.511892 1.252836e-02 64 0.493956 5.407374e-03 128 0.493635 5.728692e-03 17 0.500000 4 0.500000 0.000000e+00 8 0.500000 5.551115e-16 16 0.500000 6.661338e-16 32 0.500000 6.106227e-16 64 0.500000 1.110223e-16 128 0.500000 5.551115e-17 18 0.170557 4 0.168328 2.229126e-03 8 0.170000 5.569671e-04 16 0.170418 1.392222e-04 32 0.170523 3.480432e-05 64 0.170549 8.701004e-06 128 0.170555 2.175246e-06 19 -1.000000 4 -0.591781 4.082191e-01 8 -0.753866 2.461338e-01 16 -0.855597 1.444025e-01 32 -0.917050 8.295033e-02 64 -0.953130 4.687003e-02 128 -0.973862 2.613754e-02 20 1.564396 4 1.543702 2.069470e-02 8 1.559214 5.182230e-03 16 1.563101 1.295599e-03 32 1.564073 3.238996e-04 64 1.564315 8.097485e-05 128 1.564376 2.024371e-05 21 0.210803 4 0.207927 2.876183e-03 8 0.192954 1.784895e-02 16 0.196013 1.478933e-02 32 0.211297 4.945963e-04 64 0.207238 3.564890e-03 128 0.209774 1.029167e-03 22 0.728103 4 0.724631 3.471689e-03 8 0.727235 8.680476e-04 16 0.727886 2.170138e-04 32 0.728049 5.425347e-05 64 0.728089 1.356337e-05 128 0.728100 3.390842e-06 23 0.624713 4 0.127009 4.977039e-01 8 1.535177 9.104633e-01 16 0.634705 9.992164e-03 32 0.845949 2.212359e-01 64 1.945737 1.321024e+00 128 1.757379 1.132665e+00 24 -0.006755 4 0.030700 3.745510e-02 8 0.001096 7.850496e-03 16 -0.008059 1.304380e-03 32 -0.006778 2.353280e-05 64 -0.006729 2.539363e-05 128 -0.006690 6.467871e-05 25 -1.610864 4 -1.546000 6.486386e-02 8 -1.524319 8.654511e-02 16 -1.599206 1.165802e-02 32 -1.590384 2.048009e-02 64 -1.608240 2.624274e-03 128 -1.605817 5.047387e-03 26 7.954927 4 7.989323 3.439692e-02 8 7.954928 1.251689e-06 16 7.954927 8.881784e-16 32 7.954927 0.000000e+00 64 7.954927 0.000000e+00 128 7.954927 0.000000e+00 27 0.841117 4 0.591202 2.499153e-01 8 0.677820 1.632971e-01 16 0.734547 1.065696e-01 32 0.771716 6.940086e-02 64 0.796029 4.508758e-02 128 0.811895 2.922145e-02 28 0.019955 4 0.000000 1.995467e-02 8 0.295911 2.759558e-01 16 0.373538 3.535831e-01 32 -0.019298 3.925240e-02 64 -0.059346 7.930052e-02 128 0.008760 1.119515e-02 29 0.306853 4 0.062500 2.443528e-01 8 0.031250 2.756028e-01 16 0.015625 2.912278e-01 32 0.007812 2.990403e-01 64 0.003906 3.029466e-01 128 0.001953 3.048997e-01 30 -4.527570 4 -4.985543 4.579730e-01 8 -10.358841 5.831271e+00 16 -4.893377 3.658071e-01 32 -4.604442 7.687287e-02 64 -4.546046 1.847653e-02 128 -4.532145 4.574905e-03 31 2.651635 4 2.917647 2.660117e-01 8 2.658824 7.188202e-03 16 2.650507 1.128522e-03 32 2.651347 2.881639e-04 64 2.651563 7.207597e-05 128 2.651617 1.802118e-05 32 -12.070346 4 -13.336023 1.265677e+00 8 -12.382162 3.118161e-01 16 -12.148004 7.765778e-02 32 -12.089742 1.939580e-02 64 -12.075194 4.847783e-03 128 -12.071558 1.211873e-03 33 0.886227 4 0.636581 2.496458e-01 8 0.753713 1.325135e-01 16 0.816045 7.018186e-02 32 0.849167 3.705966e-02 64 0.866721 1.950591e-02 128 0.875994 1.023315e-02 34 1085.252667 4 1228.648500 1.433958e+02 8 1121.345766 3.609310e+01 16 1094.291200 9.038534e+00 32 1087.513254 2.260587e+00 64 1085.817873 5.652064e-01 128 1085.393972 1.413053e-01 35 26.000000 4 19.517565 6.482435e+00 8 21.745556 4.254444e+00 16 23.199637 2.800363e+00 32 23.933903 2.066097e+00 64 24.742366 1.257634e+00 128 24.903181 1.096819e+00 36 100.000000 4 1.623379 9.837662e+01 8 2.905626 9.709437e+01 16 4.454925 9.554508e+01 32 6.231542 9.376846e+01 64 8.198537 9.180146e+01 128 10.322559 8.967744e+01 37 3.135799 4 0.201389 2.934409e+00 8 0.121647 3.014152e+00 16 0.155111 2.980688e+00 32 1.780994 1.354804e+00 64 1.071146 2.064653e+00 128 1.177776 1.958022e+00 38 0.539257 4 1.943756 1.404499e+00 8 0.539747 4.901286e-04 16 0.539257 2.220446e-16 32 0.539257 3.330669e-16 64 0.539257 3.330669e-16 128 0.539257 2.220446e-16 39 2.787694 4 2.235296 5.523981e-01 8 2.405178 3.825156e-01 16 2.519288 2.684062e-01 32 2.598424 1.892698e-01 64 2.653990 1.337033e-01 128 2.693184 9.450978e-02 40 2.698957 4 2.549281 1.496758e-01 8 2.353284 3.456725e-01 16 2.399866 2.990906e-01 32 2.670544 2.841305e-02 64 2.585595 1.133614e-01 128 2.592393 1.065631e-01 41 6.095585 4 0.923760 5.171825e+00 8 1.007905 5.087680e+00 16 1.032796 5.062790e+00 32 0.957895 5.137690e+00 64 0.806324 5.289261e+00 128 0.631009 5.464576e+00 42 3.980786 4 1.881204 2.099582e+00 8 2.275754 1.705032e+00 16 2.595943 1.384843e+00 32 2.855959 1.124827e+00 64 3.067146 9.136406e-01 128 3.238680 7.421062e-01 43 2.991569 4 0.198903 2.792666e+00 8 0.074877 2.916692e+00 16 0.030610 2.960959e+00 32 0.013092 2.978477e+00 64 0.005762 2.985807e+00 128 0.002586 2.988983e+00 44 -0.030100 4 -0.094352 6.425251e-02 8 -0.050734 2.063382e-02 16 -0.035706 5.606160e-03 32 -0.031533 1.433496e-03 64 -0.030460 3.604417e-04 128 -0.030190 9.024079e-05 45 -0.292707 4 0.311944 6.046504e-01 8 0.331695 6.244017e-01 16 0.250172 5.428788e-01 32 0.178204 4.709107e-01 64 0.125742 4.184489e-01 128 0.088692 3.813990e-01 46 6.069091 4 6.072739 3.647544e-03 8 6.069092 1.095435e-06 16 6.069091 9.858780e-14 32 6.069091 1.776357e-15 64 6.069091 1.776357e-15 128 6.069091 0.000000e+00 47 -0.444444 4 -0.358104 8.634039e-02 8 -0.408090 3.635440e-02 16 -0.429475 1.496986e-02 32 -0.438389 6.054958e-03 64 -0.442031 2.413761e-03 128 -0.443494 9.507895e-04 48 -4.000000 4 -1.021258 2.978742e+00 8 -1.538192 2.461808e+00 16 -2.006772 1.993228e+00 32 -2.411783 1.588217e+00 64 -2.750468 1.249532e+00 128 -3.026987 9.730132e-01 49 52.740748 4 59.202801 6.462053e+00 8 54.841669 2.100921e+00 16 53.655409 9.146609e-01 32 52.738540 2.207992e-03 64 52.799480 5.873147e-02 128 52.797919 5.717016e-02 50 -0.128137 4 -0.274653 1.465162e-01 8 0.079820 2.079571e-01 16 -0.077041 5.109549e-02 32 -0.114029 1.410813e-02 64 -0.124197 3.939354e-03 128 -0.127043 1.093379e-03 51 -0.197814 4 -0.181006 1.680712e-02 8 -0.187048 1.076594e-02 16 -0.188652 9.161491e-03 32 -0.189093 8.720224e-03 64 -0.189220 8.594038e-03 128 -0.189257 8.556304e-03 52 -0.089944 4 -0.278683 1.887390e-01 8 -0.604948 5.150039e-01 16 0.128824 2.187679e-01 32 -0.421319 3.313749e-01 64 0.203464 2.934081e-01 128 -0.394689 3.047446e-01 53 1.504623 4 1.710578 2.059551e-01 8 1.451475 5.314778e-02 16 1.373757 1.308661e-01 32 1.392043 1.125796e-01 64 1.484043 2.057968e-02 128 1.457429 4.719423e-02 54 1.154701 4 1.166667 1.196613e-02 8 1.154762 6.136638e-05 16 1.154701 1.630567e-09 32 1.154701 2.220446e-16 64 1.154701 2.220446e-16 128 1.154701 2.220446e-16 55 0.505059 4 0.490810 1.424905e-02 8 0.501583 3.476057e-03 16 0.504195 8.640698e-04 32 0.504843 2.157150e-04 64 0.505005 5.390994e-05 128 0.505045 1.347631e-05 56 1.992252 4 1.910864 8.138879e-02 8 1.974668 1.758457e-02 16 1.987907 4.345231e-03 32 1.991169 1.083117e-03 64 1.991982 2.705816e-04 128 1.992185 6.763308e-05 57 0.400000 4 0.407018 7.018111e-03 8 0.401812 1.812465e-03 16 0.400463 4.634013e-04 32 0.400118 1.176712e-04 64 0.400030 2.973986e-05 128 0.400007 7.491909e-06 TEST06 Halton sequence rule, for 1D finite interval problems. Problem Exact Pts Approx Error 1 1.718282 1 1.648721 6.956056e-02 2 1.466373 2.519085e-01 4 1.545724 1.725580e-01 8 1.621188 9.709404e-02 16 1.667129 5.115304e-02 32 1.692066 2.621621e-02 64 1.705015 1.326657e-02 128 1.711609 6.672722e-03 2 0.700000 1 1.000000 3.000000e-01 2 0.500000 2.000000e-01 4 0.500000 2.000000e-01 8 0.625000 7.500000e-02 16 0.687500 1.250000e-02 32 0.687500 1.250000e-02 64 0.687500 1.250000e-02 128 0.695312 4.687500e-03 3 0.666667 1 0.707107 4.044011e-02 2 0.603553 6.311328e-02 4 0.606671 5.999527e-02 8 0.626880 3.978645e-02 16 0.643380 2.328693e-02 32 0.653840 1.282648e-02 64 0.659839 6.827287e-03 128 0.663108 3.558978e-03 4 0.479428 1 -0.160000 6.394282e-01 2 0.079833 3.995949e-01 4 0.349543 1.298850e-01 8 0.443181 3.624730e-02 16 0.469892 9.536647e-03 32 0.476984 2.443730e-03 64 0.478810 6.183934e-04 128 0.479273 1.555319e-04 5 1.582233 1 2.222222 6.399893e-01 2 1.935853 3.536204e-01 4 1.661369 7.913645e-02 8 1.599623 1.739026e-02 16 1.586265 4.032058e-03 32 1.583201 9.683972e-04 64 1.582470 2.371603e-04 128 1.582292 5.867420e-05 6 1.460447 1 1.414214 4.623357e-02 2 0.707107 7.533404e-01 4 1.103553 3.568937e-01 8 1.325885 1.345625e-01 16 1.405463 5.498419e-02 32 1.436734 2.371296e-02 64 1.449805 1.064218e-02 128 1.455527 4.920068e-03 7 2.000000 1 1.414214 5.857864e-01 2 1.707107 2.928932e-01 4 1.849335 1.506647e-01 8 1.920536 7.946370e-02 16 1.957052 4.294796e-02 32 1.976178 2.382233e-02 64 1.986410 1.359029e-02 128 1.992013 7.987115e-03 8 0.866973 1 0.941176 7.420348e-02 2 0.968643 1.016697e-01 4 0.924171 5.719833e-02 8 0.896917 2.994398e-02 16 0.882272 1.529929e-02 32 0.874704 7.731110e-03 64 0.870859 3.885904e-03 128 0.868921 1.948039e-03 9 1.154701 1 1.000000 1.547005e-01 2 0.833333 3.213672e-01 4 1.303396 1.486957e-01 8 1.115265 3.943579e-02 16 1.136347 1.835331e-02 32 1.148740 5.960657e-03 64 1.153008 1.692643e-03 128 1.154250 4.505883e-04 10 0.693147 1 0.666667 2.648051e-02 2 0.733333 4.018615e-02 4 0.731746 3.859885e-02 8 0.718019 2.487173e-02 16 0.707122 1.397508e-02 32 0.700540 7.392758e-03 64 0.696948 3.800384e-03 128 0.695074 1.926541e-03 11 0.379885 1 0.377541 2.344824e-03 2 0.407682 2.779659e-02 4 0.401244 2.135853e-02 8 0.392444 1.255822e-02 16 0.386635 6.749720e-03 32 0.383378 3.492567e-03 64 0.381661 1.775714e-03 128 0.380781 8.952147e-04 12 0.777505 1 0.770747 6.757593e-03 2 0.825475 4.797034e-02 4 0.815298 3.779363e-02 8 0.799976 2.247093e-02 16 0.789649 1.214426e-02 32 0.783806 6.301236e-03 64 0.780713 3.208133e-03 128 0.779123 1.618475e-03 13 1.658348 1 -1.917849 3.576196e+00 2 0.238020 1.420328e+00 4 2.329646 6.712983e-01 8 2.227107 5.687599e-01 16 1.975158 3.168100e-01 32 1.821189 1.628409e-01 64 1.740404 8.205657e-02 128 1.699475 4.112780e-02 14 0.500000 1 0.000000 5.000002e-01 2 0.000000 5.000002e-01 4 0.000000 5.000002e-01 8 0.000000 5.000002e-01 16 0.000001 4.999992e-01 32 0.047735 4.522648e-01 64 0.447443 5.255740e-02 128 0.658512 1.585118e-01 15 1.000000 1 0.000000 1.000000e+00 2 0.000000 1.000000e+00 4 0.000000 1.000000e+00 8 0.000005 9.999949e-01 16 0.006325 9.936749e-01 32 0.160317 8.396828e-01 64 0.634214 3.657855e-01 128 1.058348 5.834756e-02 16 0.499363 1 0.025424 4.739393e-01 2 0.063318 4.360456e-01 4 0.133803 3.655604e-01 8 0.260413 2.389499e-01 16 0.439725 5.963805e-02 32 0.571964 7.260064e-02 64 0.585324 8.596071e-02 128 0.551211 5.184745e-02 17 0.500000 1 0.000000 5.000000e-01 2 0.500000 0.000000e+00 4 0.625000 1.250000e-01 8 0.518306 1.830583e-02 16 0.560121 6.012124e-02 32 0.512577 1.257671e-02 64 0.513852 1.385164e-02 128 0.502590 2.590274e-03 18 0.170557 1 0.188770 1.821298e-02 2 0.149113 2.144424e-02 4 0.149360 2.119710e-02 8 0.156976 1.358159e-02 16 0.162975 7.582337e-03 32 0.166563 3.994781e-03 64 0.168508 2.049009e-03 128 0.169520 1.037499e-03 19 -1.000000 1 -0.693147 3.068528e-01 2 -1.039721 3.972077e-02 4 -1.111641 1.116413e-01 8 -1.100440 1.004398e-01 16 -1.072206 7.220596e-02 32 -1.047015 4.701477e-02 64 -1.028943 2.894294e-02 128 -1.017184 1.718416e-02 20 1.564396 1 1.990050 4.256533e-01 2 1.791838 2.274412e-01 4 1.613304 4.890801e-02 8 1.575719 1.132257e-02 16 1.567108 2.711759e-03 32 1.565059 6.628954e-04 64 1.564560 1.638376e-04 128 1.564437 4.072344e-05 21 0.210803 1 0.009866 2.009367e-01 2 0.398157 1.873541e-01 4 0.348242 1.374389e-01 8 0.216776 5.973467e-03 16 0.201803 8.999362e-03 32 0.213172 2.368996e-03 64 0.207969 2.834056e-03 128 0.210093 7.100785e-04 22 0.728103 1 0.761905 3.380185e-02 2 0.849817 1.217139e-01 4 0.804059 7.595633e-02 8 0.768413 4.031035e-02 16 0.748658 2.055528e-02 32 0.738458 1.035478e-02 64 0.733297 5.193816e-03 128 0.730704 2.600657e-03 23 0.624713 1 1.818595 1.193882e+00 2 -0.604308 1.229021e+00 4 2.000542 1.375829e+00 8 0.906778 2.820647e-01 16 1.711263 1.086550e+00 32 2.672853 2.048140e+00 64 3.381239 2.756525e+00 128 -0.244324 8.690376e-01 24 -0.006755 1 0.112539 1.192936e-01 2 0.031763 3.851761e-02 4 0.006106 1.286082e-02 8 -0.003805 2.949683e-03 16 -0.010672 3.916950e-03 32 -0.007045 2.905868e-04 64 -0.006417 3.379972e-04 128 -0.006534 2.204951e-04 25 -1.610864 1 -1.609438 1.426390e-03 2 -1.203973 4.068915e-01 4 -1.489266 1.215985e-01 8 -1.483054 1.278105e-01 16 -1.575583 3.528170e-02 32 -1.577851 3.301367e-02 64 -1.601796 9.068422e-03 128 -1.602551 8.313426e-03 26 7.954927 1 2.311455 5.643472e+00 2 4.297320 3.657607e+00 4 6.905212 1.049715e+00 8 7.798447 1.564796e-01 16 7.934611 2.031527e-02 32 7.952363 2.563894e-03 64 7.954605 3.212591e-04 128 7.954886 4.018158e-05 27 0.841117 1 0.666308 1.748089e-01 2 0.775647 6.546955e-02 4 0.821595 1.952206e-02 8 0.839814 1.302958e-03 16 0.846018 4.900708e-03 32 0.847237 6.119973e-03 64 0.846601 5.484083e-03 128 0.845455 4.338383e-03 28 0.019955 1 0.000000 1.995467e-02 2 -0.000000 1.995467e-02 4 0.716186 6.962313e-01 8 0.670908 6.509529e-01 16 0.250049 2.300947e-01 32 -0.193867 2.138214e-01 64 -0.000048 2.000252e-02 128 0.053857 3.390224e-02 29 0.306853 1 0.400000 9.314718e-02 2 0.422222 1.153694e-01 4 0.000000 3.068528e-01 8 0.000000 3.068528e-01 16 0.000000 3.068528e-01 32 0.000000 3.068528e-01 64 0.000000 3.068528e-01 128 0.000000 3.068528e-01 30 -4.527570 1 -5.483838 9.562683e-01 2 -19.923423 1.539585e+01 4 -11.149685 6.622115e+00 8 -19.651563 1.512399e+01 16 -7.416875 2.889306e+00 32 -5.710744 1.183174e+00 64 -5.139665 6.120952e-01 128 -4.848076 3.205065e-01 31 2.651635 1 8.000000 5.348365e+00 2 4.800000 2.148365e+00 4 3.000000 3.483647e-01 8 2.675472 2.383637e-02 16 2.654290 2.654734e-03 32 2.652251 6.157099e-04 64 2.651784 1.489473e-04 128 2.651672 3.663398e-05 32 -12.070346 1 0.000000 1.207035e+01 2 2.436122 1.450647e+01 4 -3.566780 8.503567e+00 8 -7.566134 4.504212e+00 16 -9.758786 2.311561e+00 32 -10.899923 1.170423e+00 64 -11.481488 5.888585e-01 128 -11.775006 2.953402e-01 33 0.886227 1 0.832555 5.367231e-02 2 1.004982 1.187554e-01 4 0.997088 1.108610e-01 8 0.961852 7.562515e-02 16 0.932398 4.617118e-02 32 0.912896 2.666953e-02 64 0.901139 1.491178e-02 128 0.894391 8.163877e-03 34 1085.252667 1 219.336000 8.659167e+02 2 111.306000 9.739467e+02 4 461.876977 6.233757e+02 8 737.968657 3.472840e+02 16 902.627981 1.826247e+02 32 991.696523 9.355614e+01 64 1037.914831 4.733784e+01 128 1061.444022 2.380864e+01 35 26.000000 1 16.159235 9.840765e+00 2 20.837103 5.162897e+00 4 26.284391 2.843905e-01 8 28.005654 2.005654e+00 16 24.604009 1.395991e+00 32 24.456862 1.543138e+00 64 24.969991 1.030009e+00 128 25.009492 9.905078e-01 36 100.000000 1 1.293458 9.870654e+01 2 3.060408 9.693959e+01 4 5.001441 9.499856e+01 8 7.108085 9.289191e+01 16 9.356215 9.064378e+01 32 11.719221 8.828078e+01 64 14.172087 8.582791e+01 128 16.692295 8.330770e+01 37 3.135799 1 0.011989 3.123809e+00 2 0.007698 3.128101e+00 4 0.199101 2.936698e+00 8 0.120456 3.015343e+00 16 0.154506 2.981292e+00 32 1.780690 1.355109e+00 64 1.070993 2.064806e+00 128 1.177700 1.958099e+00 38 0.539257 1 -0.457102 9.963588e-01 2 1.044083 5.048256e-01 4 0.375480 1.637773e-01 8 0.151004 3.882531e-01 16 0.481922 5.733448e-02 32 0.531790 7.467186e-03 64 0.538314 9.430116e-04 128 0.539139 1.181787e-04 39 2.787694 1 2.449490 3.382040e-01 2 2.956796 1.691020e-01 4 2.413419 3.742750e-01 8 2.460571 3.271231e-01 16 2.540602 2.470913e-01 32 2.607666 1.800282e-01 64 2.658277 1.294171e-01 128 2.695246 9.244812e-02 40 2.698957 1 1.871865 8.270921e-01 2 1.619264 1.079693e+00 4 2.446037 2.529192e-01 8 2.294863 4.040938e-01 16 2.369116 3.298404e-01 32 2.654802 4.415503e-02 64 2.577635 1.213221e-01 128 2.588391 1.105656e-01 41 6.095585 1 1.777778 4.317807e+00 2 0.888889 5.206696e+00 4 0.444444 5.651141e+00 8 0.222222 5.873363e+00 16 0.111111 5.984474e+00 32 0.055556 6.040030e+00 64 0.027778 6.067807e+00 128 0.013889 6.081696e+00 42 3.980786 1 2.002075 1.978711e+00 2 2.539554 1.441232e+00 4 2.917661 1.063125e+00 8 3.175552 8.052343e-01 16 3.356778 6.240087e-01 32 3.489137 4.916488e-01 64 3.589082 3.917042e-01 128 3.666450 3.143359e-01 43 2.991569 1 1.292475 1.699094e+00 2 0.646238 2.345331e+00 4 0.323119 2.668450e+00 8 0.161559 2.830010e+00 16 0.080780 2.910789e+00 32 0.040390 2.951179e+00 64 0.020195 2.971374e+00 128 0.010097 2.981472e+00 44 -0.030100 1 0.000041 3.014098e-02 2 0.000021 3.012047e-02 4 0.000248 3.034780e-02 8 -0.003433 2.666634e-02 16 -0.012056 1.804392e-02 32 -0.019708 1.039154e-02 64 -0.024548 5.552078e-03 128 -0.027234 2.866019e-03 45 -0.292707 1 -0.832294 5.395870e-01 2 -0.416147 1.234401e-01 4 -0.208073 8.463329e-02 8 -0.104037 1.886700e-01 16 -0.052018 2.406884e-01 32 -0.026009 2.666975e-01 64 -0.013005 2.797021e-01 128 -0.006502 2.862044e-01 46 6.069091 1 4.656977 1.412114e+00 2 5.259634 8.094565e-01 4 5.889265 1.798260e-01 8 6.043492 2.559851e-02 16 6.065796 3.294769e-03 32 6.068676 4.149125e-04 64 6.069039 5.196072e-05 128 6.069084 6.498117e-06 47 -0.444444 1 -0.490129 4.568463e-02 2 -0.591638 1.471937e-01 4 -0.541902 9.745802e-02 8 -0.494733 5.028899e-02 16 -0.467766 2.332147e-02 32 -0.454635 1.019068e-02 64 -0.448732 4.287223e-03 128 -0.446201 1.756817e-03 48 -4.000000 1 -0.980258 3.019742e+00 2 -1.876423 2.123577e+00 4 -2.491646 1.508354e+00 8 -2.924486 1.075514e+00 16 -3.232095 7.679049e-01 32 -3.451504 5.484958e-01 64 -3.608194 3.918057e-01 128 -3.720134 2.798660e-01 49 52.740748 1 -11.776902 6.451765e+01 2 -6.181932 5.892268e+01 4 18.464652 3.427610e+01 8 34.464907 1.827584e+01 16 43.466343 9.274405e+00 32 47.643961 5.096787e+00 64 50.252187 2.488561e+00 128 51.524272 1.216476e+00 50 -0.128137 1 -0.000000 1.281368e-01 2 -0.693147 5.650103e-01 4 0.092944 2.210806e-01 8 -0.240372 1.122351e-01 16 -0.257145 1.290079e-01 32 -0.175294 4.715699e-02 64 -0.142619 1.448170e-02 128 -0.132347 4.209659e-03 51 -0.197814 1 -0.316254 1.184406e-01 2 -0.239320 4.150694e-02 4 -0.199346 1.532829e-03 8 -0.191640 6.173633e-03 16 -0.189932 7.882014e-03 32 -0.189482 8.331984e-03 64 -0.189345 8.468169e-03 128 -0.189300 8.513326e-03 52 -0.089944 1 0.065217 1.551614e-01 2 0.938269 1.028213e+00 4 -0.542113 4.521693e-01 8 -0.481150 3.912058e-01 16 0.177168 2.671118e-01 32 -0.418401 3.284571e-01 64 0.191450 2.813936e-01 128 -0.406989 3.170451e-01 53 1.504623 1 1.154701 3.499222e-01 2 0.994379 5.102437e-01 4 1.687021 1.823984e-01 8 1.436163 6.845962e-02 16 1.365322 1.393006e-01 32 1.387643 1.169800e-01 64 1.481798 2.282432e-02 128 1.456295 4.832751e-02 54 1.154701 1 1.000000 1.547005e-01 2 0.833333 3.213672e-01 4 1.303396 1.486957e-01 8 1.115265 3.943579e-02 16 1.136347 1.835331e-02 32 1.148740 5.960657e-03 64 1.153008 1.692643e-03 128 1.154250 4.505883e-04 55 0.505059 1 0.569783 6.472419e-02 2 0.337591 1.674676e-01 4 0.426228 7.883082e-02 8 0.467352 3.770701e-02 16 0.486789 1.826964e-02 32 0.496085 8.973755e-03 64 0.500614 4.444947e-03 128 0.502847 2.211794e-03 56 1.992252 1 2.222222 2.299698e-01 2 2.203261 2.110089e-01 4 2.111537 1.192845e-01 8 2.028439 3.618707e-02 16 2.001285 9.032624e-03 32 1.994474 2.221457e-03 64 1.992801 5.488011e-04 128 1.992389 1.362654e-04 57 0.400000 1 0.353553 4.644661e-02 2 0.239277 1.607233e-01 4 0.293067 1.069333e-01 8 0.341266 5.873441e-02 16 0.369559 3.044133e-02 32 0.384554 1.544629e-02 64 0.392228 7.771971e-03 128 0.396103 3.896851e-03 TEST07 Evenly spaced point sequence rule, for 1D finite interval problems. Problem Exact Pts Approx Error 1 1.718282 1 1.648721 6.956056e-02 2 1.859141 1.408591e-01 4 1.765407 4.712525e-02 8 1.738445 2.016348e-02 16 1.727682 9.400274e-03 32 1.722828 4.546189e-03 64 1.720518 2.236436e-03 128 1.719391 1.109270e-03 2 0.700000 1 1.000000 3.000000e-01 2 0.500000 2.000000e-01 4 0.750000 5.000000e-02 8 0.625000 7.500000e-02 16 0.687500 1.250000e-02 32 0.687500 1.250000e-02 64 0.703125 3.125000e-03 128 0.695312 4.687500e-03 3 0.666667 1 0.707107 4.044011e-02 2 0.500000 1.666667e-01 4 0.598462 6.820495e-02 8 0.636755 2.991118e-02 16 0.653069 1.359781e-02 32 0.660334 6.333127e-03 64 0.663664 3.003070e-03 128 0.665223 1.443637e-03 4 0.479428 1 -0.160000 6.394282e-01 2 1.758664 1.279236e+00 4 0.905961 4.265328e-01 8 0.662218 1.827894e-01 16 0.564721 8.529274e-02 32 0.520696 4.126821e-02 64 0.499734 2.030595e-02 128 0.489501 1.007288e-02 5 1.582233 1 2.222222 6.399893e-01 2 0.689655 8.925778e-01 4 1.321908 2.603246e-01 8 1.462178 1.200547e-01 16 1.524466 5.776743e-02 32 1.553860 2.837249e-02 64 1.568168 1.406449e-02 128 1.575230 7.002522e-03 6 1.460447 1 1.414214 4.623357e-02 2 1.931852 4.714045e-01 4 1.626485 1.660383e-01 8 1.531748 7.130072e-02 16 1.493423 3.297614e-02 32 1.476237 1.578962e-02 64 1.468145 7.697627e-03 128 1.464237 3.790140e-03 7 2.000000 1 1.414214 5.857864e-01 2 0.500000 1.500000e+00 4 0.989199 1.010801e+00 8 1.328790 6.712100e-01 16 1.552581 4.474191e-01 32 1.698992 3.010079e-01 64 1.795440 2.045604e-01 128 1.859706 1.402944e-01 8 0.866973 1 0.941176 7.420348e-02 2 0.750000 1.169730e-01 4 0.830714 3.625888e-02 8 0.850860 1.611275e-02 16 0.859315 7.658188e-03 32 0.863234 3.739420e-03 64 0.865125 1.848371e-03 128 0.866054 9.189778e-04 9 1.154701 1 1.000000 1.547005e-01 2 1.000000 1.547005e-01 4 1.115385 3.931592e-02 8 1.135363 1.933759e-02 16 1.144231 1.046977e-02 32 1.149866 4.834392e-03 64 1.152283 2.417196e-03 128 1.153492 1.208598e-03 10 0.693147 1 0.666667 2.648051e-02 2 0.750000 5.685282e-02 4 0.712500 1.935282e-02 8 0.701367 8.219855e-03 16 0.696961 3.813574e-03 32 0.694987 1.839646e-03 64 0.694051 9.038258e-04 128 0.693595 4.480074e-04 11 0.379885 1 0.377541 2.344824e-03 2 0.384471 4.585218e-03 4 0.381404 1.518218e-03 8 0.380538 6.526442e-04 16 0.380191 3.051159e-04 32 0.380033 1.477731e-04 64 0.379958 7.274746e-05 128 0.379922 3.609570e-05 12 0.777505 1 0.770747 6.757593e-03 2 0.790988 1.348372e-02 4 0.781996 4.491472e-03 8 0.779430 1.925514e-03 16 0.778403 8.987412e-04 32 0.777940 4.349166e-04 64 0.777719 2.140169e-04 128 0.777611 1.061684e-04 13 1.658348 1 -1.917849 3.576196e+00 2 4.727989 3.069642e+00 4 2.361375 7.030279e-01 8 2.030047 3.716991e-01 16 1.847459 1.891118e-01 32 1.753614 9.526623e-02 64 1.706149 4.780092e-02 128 1.682289 2.394135e-02 14 0.500000 1 0.000000 5.000002e-01 2 35.355339 3.485534e+01 4 17.677670 1.717767e+01 8 8.838835 8.338835e+00 16 4.419417 3.919417e+00 32 2.209709 1.709709e+00 64 1.125966 6.259655e-01 128 0.772347 2.723465e-01 15 1.000000 1 0.000000 1.000000e+00 2 125.000000 1.240000e+02 4 62.500000 6.150000e+01 8 31.250000 3.025000e+01 16 15.625001 1.462500e+01 32 7.814958 6.814958e+00 64 3.981526 2.981526e+00 128 2.270193 1.270193e+00 16 0.499363 1 0.025424 4.739393e-01 2 7.960929 7.461566e+00 4 3.998315 3.498951e+00 8 2.047575 1.548211e+00 16 1.128165 6.288012e-01 32 0.747092 2.477282e-01 64 0.610670 1.113065e-01 128 0.551973 5.260956e-02 17 0.500000 1 0.000000 5.000000e-01 2 0.000000 5.000000e-01 4 0.375000 1.250000e-01 8 0.437500 6.250000e-02 16 0.468750 3.125000e-02 32 0.484375 1.562500e-02 64 0.492188 7.812500e-03 128 0.496094 3.906250e-03 18 0.170557 1 0.188770 1.821298e-02 2 0.134471 3.608664e-02 4 0.158562 1.199557e-02 8 0.165410 5.147400e-03 16 0.168153 2.403920e-03 32 0.169394 1.163635e-03 64 0.169985 5.726928e-04 128 0.170273 2.841192e-04 19 -1.000000 1 -0.693147 3.068528e-01 2 0.000000 1.000000e+00 4 -0.376019 6.239807e-01 8 -0.637026 3.629738e-01 16 -0.795093 2.049074e-01 32 -0.886293 1.137069e-01 64 -0.937628 6.237232e-02 128 -0.966081 3.391944e-02 20 1.564396 1 1.990050 4.256533e-01 2 0.997506 5.668902e-01 4 1.394721 1.696752e-01 8 1.487613 7.678366e-02 16 1.527584 3.681261e-02 32 1.546347 1.804967e-02 64 1.555457 8.939920e-03 128 1.559947 4.449233e-03 21 0.210803 1 0.009866 2.009367e-01 2 0.035326 1.754771e-01 4 0.078499 1.323033e-01 8 0.170559 4.024388e-02 16 0.310878 1.000748e-01 32 0.193596 1.720640e-02 64 0.207936 2.866316e-03 128 0.208410 2.393123e-03 22 0.728103 1 0.761905 3.380185e-02 2 0.666667 6.143625e-02 4 0.708116 1.998647e-02 8 0.719431 8.671579e-03 16 0.724032 4.071247e-03 32 0.726127 1.975886e-03 64 0.727129 9.737200e-04 128 0.727620 4.833882e-04 23 0.624713 1 1.818595 1.193882e+00 2 0.420735 2.039778e-01 4 0.690268 6.555512e-02 8 1.259266 6.345526e-01 16 1.492156 8.674432e-01 32 0.177477 4.472359e-01 64 1.062671 4.379575e-01 128 1.758547 1.133834e+00 24 -0.006755 1 0.112539 1.192936e-01 2 0.079577 8.633217e-02 4 0.048197 5.495173e-02 8 0.000000 6.754846e-03 16 0.002885 9.639563e-03 32 -0.003858 2.896997e-03 64 -0.005620 1.135126e-03 128 -0.006105 6.493185e-04 25 -1.610864 1 -1.609438 1.426390e-03 2 -0.780324 8.305404e-01 4 -1.491287 1.195775e-01 8 -1.560150 5.071394e-02 16 -1.513982 9.688189e-02 32 -1.569472 4.139217e-02 64 -1.605308 5.556671e-03 128 -1.608111 2.753540e-03 26 7.954927 1 2.311455 5.643472e+00 2 17.079468 9.124542e+00 4 10.445206 2.490280e+00 8 9.095512 1.140585e+00 16 8.525210 5.702839e-01 32 8.240068 2.851419e-01 64 8.097497 1.425710e-01 128 8.026212 7.128548e-02 27 0.841117 1 0.666308 1.748089e-01 2 0.250000 5.911169e-01 4 0.469662 3.714545e-01 8 0.612128 2.289894e-01 16 0.700205 1.409123e-01 32 0.754075 8.704187e-02 64 0.787059 5.405754e-02 128 0.807363 3.375428e-02 28 0.019955 1 0.000000 1.995467e-02 2 0.000000 1.995467e-02 4 -0.146891 1.668453e-01 8 0.379678 3.597231e-01 16 0.106812 8.685716e-02 32 -0.035872 5.582634e-02 64 -0.064245 8.419944e-02 128 0.008494 1.146113e-02 29 0.306853 1 0.400000 9.314718e-02 2 0.000000 3.068528e-01 4 0.000000 3.068528e-01 8 0.000000 3.068528e-01 16 0.000000 3.068528e-01 32 0.000000 3.068528e-01 64 0.000000 3.068528e-01 128 0.000000 3.068528e-01 30 -4.527570 1 -5.483838 9.562683e-01 2 23.363250 2.789082e+01 4 5.223729 9.751298e+00 8 26.816814 3.134438e+01 16 -3.188586 1.338984e+00 32 -3.735613 7.919565e-01 64 -4.110553 4.170165e-01 128 -4.314284 2.132859e-01 31 2.651635 1 8.000000 5.348365e+00 2 0.470588 2.181047e+00 4 1.675294 9.763412e-01 8 2.351374 3.002611e-01 16 2.514048 1.375872e-01 32 2.583180 6.845517e-02 64 2.617483 3.415208e-02 128 2.634578 1.705759e-02 32 -12.070346 1 0.000000 1.207035e+01 2 -34.778519 2.270817e+01 4 -19.459127 7.388780e+00 8 -15.265777 3.195431e+00 16 -13.572457 1.502110e+00 32 -12.799999 7.296523e-01 64 -12.430086 3.597399e-01 128 -12.248975 1.786290e-01 33 0.886227 1 0.832555 5.367231e-02 2 0.000000 8.862269e-01 4 0.421227 4.649998e-01 8 0.644434 2.417928e-01 16 0.761023 1.252042e-01 32 0.821563 6.466430e-02 64 0.852896 3.333118e-02 128 0.869076 1.715142e-02 34 1085.252667 1 219.336000 8.659167e+02 2 3067.086000 1.981833e+03 4 1770.555136 6.853025e+02 8 1374.202618 2.889500e+02 16 1218.757605 1.335049e+02 32 1149.518446 6.426578e+01 64 1116.792990 3.154032e+01 128 1100.878158 1.562549e+01 35 26.000000 1 16.159235 9.840765e+00 2 23.616667 2.383333e+00 4 20.435678 5.564322e+00 8 21.324608 4.675392e+00 16 23.718053 2.281947e+00 32 23.739622 2.260378e+00 64 25.112786 8.872145e-01 128 24.869005 1.130995e+00 36 100.000000 1 1.293458 9.870654e+01 2 0.000000 1.000000e+02 4 0.884241 9.911576e+01 8 2.307015 9.769298e+01 16 4.031697 9.596830e+01 32 5.953683 9.404632e+01 64 8.024609 9.197539e+01 128 10.217309 8.978269e+01 37 3.135799 1 0.011989 3.123809e+00 2 0.011394 3.124405e+00 4 0.024209 3.111590e+00 8 0.055103 3.080695e+00 16 0.329992 2.805807e+00 32 0.360474 2.775324e+00 64 0.587094 2.548705e+00 128 1.985503 1.150296e+00 38 0.539257 1 -0.457102 9.963588e-01 2 3.141593 2.602336e+00 4 2.826002 2.286745e+00 8 0.870153 3.308956e-01 16 0.701903 1.626460e-01 32 0.620580 8.132299e-02 64 0.579918 4.066150e-02 128 0.559588 2.033075e-02 39 2.787694 1 2.449490 3.382040e-01 2 1.478398 1.309296e+00 4 1.172212 1.615482e+00 8 2.265288 5.224058e-01 16 1.997653 7.900407e-01 32 2.560475 2.272182e-01 64 2.404938 3.827556e-01 128 2.683325 1.043690e-01 40 2.698957 1 1.871865 8.270921e-01 2 1.643517 1.055439e+00 4 1.919117 7.798393e-01 8 2.158562 5.403948e-01 16 2.453254 2.457029e-01 32 2.475271 2.236860e-01 64 2.532539 1.664178e-01 128 2.614038 8.491855e-02 41 6.095585 1 1.777778 4.317807e+00 2 0.000000 6.095585e+00 4 0.000000 6.095585e+00 8 0.000000 6.095585e+00 16 0.000000 6.095585e+00 32 0.000000 6.095585e+00 64 0.000000 6.095585e+00 128 0.000000 6.095585e+00 42 3.980786 1 2.002075 1.978711e+00 2 0.785398 3.195388e+00 4 1.464939 2.515847e+00 8 2.028449 1.952338e+00 16 2.457399 1.523387e+00 32 2.780825 1.199961e+00 64 3.027234 9.535521e-01 128 3.217779 7.630070e-01 43 2.991569 1 1.292475 1.699094e+00 2 0.000000 2.991569e+00 4 0.000000 2.991569e+00 8 0.000000 2.991569e+00 16 0.000000 2.991569e+00 32 0.000000 2.991569e+00 64 0.000000 2.991569e+00 128 0.000000 2.991569e+00 44 -0.030100 1 0.000041 3.014098e-02 2 -0.378401 3.483015e-01 4 -0.189055 1.589550e-01 8 -0.096497 6.639768e-02 16 -0.057824 2.772451e-02 32 -0.042463 1.236342e-02 64 -0.035908 5.808352e-03 128 -0.032912 2.812056e-03 45 -0.292707 1 -0.832294 5.395870e-01 2 0.000000 2.927067e-01 4 0.000000 2.927067e-01 8 0.000000 2.927067e-01 16 0.000000 2.927067e-01 32 0.000000 2.927067e-01 64 0.000000 2.927067e-01 128 0.000000 2.927067e-01 46 6.069091 1 4.656977 1.412114e+00 2 7.909393 1.840302e+00 4 6.549987 4.808962e-01 8 6.299136 2.300451e-01 16 6.184110 1.150189e-01 32 6.126600 5.750945e-02 64 6.097846 2.875472e-02 128 6.083468 1.437736e-02 47 -0.444444 1 -0.490129 4.568463e-02 2 0.000000 4.444444e-01 4 -0.241336 2.031082e-01 8 -0.351240 9.320469e-02 16 -0.401411 4.303310e-02 32 -0.424439 2.000501e-02 64 -0.435073 9.371004e-03 128 -0.440019 4.425637e-03 48 -4.000000 1 -0.980258 3.019742e+00 2 0.000000 4.000000e+00 4 -0.599861 3.400139e+00 8 -1.261411 2.738589e+00 16 -1.842848 2.157152e+00 32 -2.319859 1.680141e+00 64 -2.700621 1.299379e+00 128 -3.000553 9.994466e-01 49 52.740748 1 -11.776902 6.451765e+01 2 163.026743 1.102860e+02 4 92.263929 3.952318e+01 8 69.436515 1.669577e+01 16 60.224989 7.484241e+00 32 56.518783 3.778035e+00 64 54.751230 2.010482e+00 128 53.607414 8.666653e-01 50 -0.128137 1 -0.000000 1.281368e-01 2 0.000000 1.281368e-01 4 0.150071 2.782076e-01 8 0.140544 2.686811e-01 16 -0.065993 6.214353e-02 32 -0.109643 1.849418e-02 64 -0.122143 5.994159e-03 128 -0.126035 2.101807e-03 51 -0.197814 1 -0.316254 1.184406e-01 2 0.000000 1.978136e-01 4 -0.131153 6.666069e-02 8 -0.163113 3.470009e-02 16 -0.176789 2.102470e-02 32 -0.183174 1.463943e-02 64 -0.186262 1.155206e-02 128 -0.187778 1.003510e-02 52 -0.089944 1 0.065217 1.551614e-01 2 -2.999049 2.909105e+00 4 -1.359615 1.269671e+00 8 -1.468146 1.378202e+00 16 -0.357605 2.676610e-01 32 -1.089059 9.991148e-01 64 -0.144402 5.445846e-02 128 -1.014948 9.250043e-01 53 1.504623 1 1.154701 3.499222e-01 2 0.853553 6.510694e-01 4 1.183240 3.213825e-01 8 1.408103 9.652003e-02 16 2.020843 5.162206e-01 32 1.389216 1.154068e-01 64 1.493769 1.085403e-02 128 1.636591 1.319678e-01 54 1.154701 1 1.000000 1.547005e-01 2 1.000000 1.547005e-01 4 1.115385 3.931592e-02 8 1.135363 1.933759e-02 16 1.144231 1.046977e-02 32 1.149866 4.834392e-03 64 1.152283 2.417196e-03 128 1.153492 1.208598e-03 55 0.505059 1 0.569783 6.472419e-02 2 0.288056 2.170024e-01 4 0.431284 7.377438e-02 8 0.473951 3.110739e-02 16 0.490574 1.448456e-02 32 0.498055 7.004004e-03 64 0.501613 3.445428e-03 128 0.503350 1.708913e-03 56 1.992252 1 2.222222 2.299698e-01 2 1.052632 9.396208e-01 4 1.635736 3.565164e-01 8 1.854581 1.376714e-01 16 1.928889 6.336374e-02 32 1.961771 3.048128e-02 64 1.977296 1.495645e-02 128 1.984843 7.408953e-03 57 0.400000 1 0.353553 4.644661e-02 2 0.500000 1.000000e-01 4 0.434195 3.419529e-02 8 0.414560 1.456032e-02 16 0.406743 6.743425e-03 32 0.403246 3.246394e-03 64 0.401593 1.592706e-03 128 0.400789 7.888004e-04 test_int_test Normal end of execution. 28-Mar-2019 12:32:19