23 February 2013 12:37:19.736 PM TEST_ODE_PRB FORTRAN90 version Test the TEST_ODE library. TEST01 List the problem titles and sizes. There are 40 test problems. Test Size Title 1 1 Problem p01, Enright and Pryce #A1, exponential decay. 2 1 Problem p02, Enright and Pryce #A2 3 1 Problem p03, Enright and Pryce #A3 4 1 Problem p04, Enright and Pryce #A4 5 1 Problem p05, Enright and Pryce #A5 6 2 Problem p06, Enright and Pryce #B1 7 3 Problem p07, Enright and Pryce #B2 8 3 Problem p08, Enright and Pryce #B3 9 3 Problem p09, Enright and Pryce #B4 10 3 Problem p10, Enright and Pryce #B5 11 10 Problem p11, Enright and Pryce #C1 12 10 Problem p12, Enright and Pryce #C2 13 10 Problem p13, Enright and Pryce #C3 14 51 Problem p14, Enright and Pryce #C4 15 30 Problem p15, Enright and Pryce #C5 16 4 Problem p16, Enright and Pryce #D1 17 4 Problem p17, Enright and Pryce #D2 18 4 Problem p18, Enright and Pryce #D3 19 4 Problem p19, Enright and Pryce #D4 20 4 Problem p20, Enright and Pryce #D5 21 2 Problem p21, Enright and Pryce #E1 22 2 Problem p22, Enright and Pryce #E2 23 2 Problem p23, Enright and Pryce #E3 24 2 Problem p24, Enright and Pryce #E4 25 2 Problem p25, Enright and Pryce #E5 26 2 Problem p26, Enright and Pryce #F1 27 1 Problem p27, Enright and Pryce #F2 28 2 Problem p28, Enright and Pryce #F3 29 1 Problem p29, Enright and Pryce #F4 30 1 Problem p30, Enright and Pryce #F5 31 2 Problem p31, Lotka-Volterra Predator-Prey Equations. 32 3 Problem p32, The Lorenz System 33 2 Problem p33, The Van der Pol equation 34 2 Problem p34, The Linearized Damped Pendulum 35 2 Problem p35, The Nonlinear Damped Pendulum 36 2 Problem p36, Duffing's Equation 37 2 Problem p37, Duffing's Equation with Damping and Forcing 38 1 Problem p38, Shampine's Ball of Flame 39 1 Problem p39, Polking's first order ODE 40 1 Problem p40, the Knee problem TEST02 Solve problems using an Euler method. The number of steps taken is 500 The number of tests available is 40 EULER_TEST Problem number = 1 Problem p01, Enright and Pryce #A1, exponential decay. The system is autonomous. Number of equations is 1 Stepsize H = 0.400000E-01 0.00000 1.00000 2.00000 0.129886 4.00000 0.168703E-01 6.00000 0.219121E-02 8.00000 0.284608E-03 10.0000 0.369665E-04 12.0000 0.480142E-05 14.0000 0.623637E-06 16.0000 0.810015E-07 18.0000 0.105209E-07 20.0000 0.136652E-08 Expected final conditions: 20.0000 0.206115E-08 EULER_TEST Problem number = 2 Problem p02, Enright and Pryce #A2 The system is autonomous. Number of equations is 1 Stepsize H = 0.400000E-01 0.00000 1.00000 2.00000 0.574140 4.00000 0.445039 6.00000 0.376380 8.00000 0.332107 10.0000 0.300521 12.0000 0.276526 14.0000 0.257497 16.0000 0.241927 18.0000 0.228881 20.0000 0.217742 Expected final conditions: 20.0000 0.218218 EULER_TEST Problem number = 3 Problem p03, Enright and Pryce #A3 The system is not autonomous. Number of equations is 1 Stepsize H = 0.400000E-01 0.00000 1.00000 2.00000 2.51256 4.00000 0.463410 6.00000 0.714545 8.00000 2.54340 10.0000 0.542180 12.0000 0.522416 14.0000 2.37804 16.0000 0.662504 18.0000 0.398605 20.0000 2.05617 Expected final conditions: 20.0000 2.49165 EULER_TEST Problem number = 4 Problem p04, Enright and Pryce #A4 The system is autonomous. Number of equations is 1 Stepsize H = 0.400000E-01 0.00000 1.00000 2.00000 1.59374 4.00000 2.49413 6.00000 3.79908 8.00000 5.57108 10.0000 7.77540 12.0000 10.2363 14.0000 12.6717 16.0000 14.8100 18.0000 16.4983 20.0000 17.7226 Expected final conditions: 20.0000 17.7302 EULER_TEST Problem number = 5 Problem p05, Enright and Pryce #A5 The system is not autonomous. Number of equations is 1 Stepsize H = 0.400000E-01 0.00000 4.00000 2.00000 5.36857 4.00000 6.01242 6.00000 6.22849 8.00000 6.11335 10.0000 5.70801 12.0000 5.02812 14.0000 4.07339 16.0000 2.83008 18.0000 1.26979 20.0000 -0.655739 Expected final conditions: 20.0000 -0.788783 EULER_TEST Problem number = 6 Problem p06, Enright and Pryce #B1 The system is autonomous. Number of equations is 2 Stepsize H = 0.400000E-01 0.00000 1.00000 3.00000 2.00000 0.688726E-01 0.549361 4.00000 1.18048 0.144933 6.00000 0.126499 2.94146 8.00000 0.312197E-01 0.408280 10.0000 0.723914 0.797740E-01 12.0000 0.350035 4.45735 14.0000 0.355625E-02 0.617137 16.0000 0.605577E-01 0.830686E-01 18.0000 2.41756 0.372902E-01 20.0000 0.917584E-03 3.11114 Expected final conditions: 20.0000 0.676188 0.186082 EULER_TEST Problem number = 7 Problem p07, Enright and Pryce #B2 The system is autonomous. Number of equations is 3 Stepsize H = 0.400000E-01 0.00000 2.00000 0.00000 1.00000 2.00000 1.06578 0.998325 0.935895 4.00000 1.00844 0.999997 0.991566 6.00000 1.00110 1.00000 0.998904 8.00000 1.00014 1.00000 0.999858 10.0000 1.00002 1.00000 0.999982 12.0000 1.00000 1.00000 0.999998 14.0000 1.00000 1.00000 1.00000 16.0000 1.00000 1.00000 1.00000 18.0000 1.00000 1.00000 1.00000 20.0000 1.00000 1.00000 1.00000 Expected final conditions: 20.0000 1.00000 1.00000 1.00000 EULER_TEST Problem number = 8 Problem p08, Enright and Pryce #B3 The system is autonomous. Number of equations is 3 Stepsize H = 0.400000E-01 0.00000 1.00000 0.00000 0.00000 2.00000 0.129886 0.479223 0.390891 4.00000 0.168703E-01 0.294023 0.689107 6.00000 0.219121E-02 0.192988 0.804820 8.00000 0.284608E-03 0.140272 0.859443 10.0000 0.369665E-04 0.109604 0.890359 12.0000 0.480142E-05 0.898588E-01 0.910136 14.0000 0.623637E-06 0.761346E-01 0.923865 16.0000 0.810015E-07 0.660492E-01 0.933951 18.0000 0.105209E-07 0.583254E-01 0.941675 20.0000 0.136652E-08 0.522204E-01 0.947780 Expected final conditions: 20.0000 0.206115E-08 0.525723E-01 0.947428 EULER_TEST Problem number = 9 Problem p09, Enright and Pryce #B4 The system is autonomous. Number of equations is 3 Stepsize H = 0.400000E-01 0.00000 3.00000 0.00000 0.00000 2.00000 -0.739391 1.51940 0.923267 4.00000 -0.913878 -1.12595 -0.743785 6.00000 3.01820 -0.876938 -0.275834 8.00000 -0.348920 2.13445 1.00711 10.0000 -1.20703 -0.838989 -0.528146 12.0000 2.71324 -1.71877 -0.528275 14.0000 0.335416 2.62442 1.00943 16.0000 -1.48062 -0.497059 -0.268500 18.0000 2.13470 -2.41007 -0.737210 20.0000 1.25686 2.85378 0.930950 Expected final conditions: 20.0000 0.982695 2.19845 0.912945 EULER_TEST Problem number = 10 Problem p10, Enright and Pryce #B5 The system is autonomous. Number of equations is 3 Stepsize H = 0.400000E-01 0.00000 0.00000 1.00000 1.00000 2.00000 1.02370 -0.102548 0.695452 4.00000 -0.290064 -1.02092 1.00023 6.00000 -1.04434 0.307592 0.708338 8.00000 0.592492 0.958292 0.956122 10.0000 1.02434 -0.528044 0.754528 12.0000 -0.872562 -0.817636 0.872513 14.0000 -0.950343 0.766225 0.835960 16.0000 1.10537 0.622348 0.767971 18.0000 0.799459 -1.01837 0.948477 20.0000 -1.28390 -0.400900 0.666120 Expected final conditions: 20.0000 -0.939657 -0.342118 0.741413 EULER_TEST Problem number = 11 Problem p11, Enright and Pryce #C1 The system is autonomous. Number of equations is 10 The system is large. Print only MIN, AVERAGE, MAX, L2NORM Stepsize H = 0.400000E-01 0.00000 0.00000 0.100000 1.00000 1.00000 2.00000 0.147903E-03 0.100000 0.276233 0.457994 4.00000 0.168703E-01 0.100000 0.199388 0.382230 6.00000 0.219121E-02 0.100000 0.163932 0.365608 8.00000 0.284608E-03 0.100000 0.407433 0.483293 10.0000 0.369665E-04 0.100000 0.671789 0.691172 12.0000 0.480142E-05 0.100000 0.850291 0.854231 14.0000 0.623637E-06 0.100000 0.941604 0.942239 16.0000 0.810015E-07 0.100000 0.979907 0.979988 18.0000 0.105209E-07 0.100000 0.993753 0.993762 20.0000 0.136652E-08 0.100000 0.998213 0.998214 Expected final conditions: 20.0000 0.206115E-08 0.100000 0.997913 0.997914 EULER_TEST Problem number = 12 Problem p12, Enright and Pryce #C2 The system is autonomous. Number of equations is 10 The system is large. Print only MIN, AVERAGE, MAX, L2NORM Stepsize H = 0.400000E-01 0.00000 0.00000 0.100000 1.00000 1.00000 2.00000 0.448410E-01 0.100000 0.265996 0.370675 4.00000 0.150337E-01 0.100000 0.856546 0.857882 6.00000 0.216175E-02 0.100000 0.980412 0.980434 8.00000 0.284150E-03 0.100000 0.997441 0.997441 10.0000 0.369594E-04 0.100000 0.999667 0.999667 12.0000 0.480131E-05 0.100000 0.999957 0.999957 14.0000 0.623635E-06 0.100000 0.999994 0.999994 16.0000 0.810015E-07 0.100000 0.999999 0.999999 18.0000 0.105209E-07 0.100000 1.00000 1.00000 20.0000 0.136652E-08 0.100000 1.00000 1.00000 Expected final conditions: 20.0000 0.206115E-08 0.100000 1.00000 1.00000 EULER_TEST Problem number = 13 Problem p13, Enright and Pryce #C3 The system is autonomous. Number of equations is 10 The system is large. Print only MIN, AVERAGE, MAX, L2NORM Stepsize H = 0.400000E-01 0.00000 0.00000 0.100000 1.00000 1.00000 2.00000 0.275836E-04 0.383311E-01 0.116251 0.181551 4.00000 0.825960E-03 0.275992E-01 0.590711E-01 0.109812 6.00000 0.250267E-02 0.223462E-01 0.391706E-01 0.813787E-01 8.00000 0.379007E-02 0.187258E-01 0.299552E-01 0.652767E-01 10.0000 0.432783E-02 0.158534E-01 0.237043E-01 0.541932E-01 12.0000 0.432477E-02 0.134619E-01 0.197191E-01 0.456423E-01 14.0000 0.403323E-02 0.114411E-01 0.165891E-01 0.386623E-01 16.0000 0.362103E-02 0.972617E-02 0.140063E-01 0.328237E-01 18.0000 0.318089E-02 0.826888E-02 0.118553E-01 0.278911E-01 20.0000 0.275861E-02 0.703009E-02 0.100512E-01 0.237078E-01 Expected final conditions: 20.0000 0.276243E-02 0.704861E-02 0.100794E-01 0.237705E-01 EULER_TEST Problem number = 14 Problem p14, Enright and Pryce #C4 The system is autonomous. Number of equations is 51 The system is large. Print only MIN, AVERAGE, MAX, L2NORM Stepsize H = 0.400000E-01 0.00000 0.00000 0.196078E-01 1.00000 1.00000 2.00000 0.126765E-69 0.751604E-02 0.116251 0.181551 4.00000 0.215779E-42 0.542369E-02 0.590711E-01 0.109815 6.00000 0.865576E-33 0.445780E-02 0.391710E-01 0.814743E-01 8.00000 0.465688E-27 0.387325E-02 0.299702E-01 0.658449E-01 10.0000 0.389432E-23 0.347114E-02 0.237673E-01 0.557905E-01 12.0000 0.296960E-20 0.317283E-02 0.200308E-01 0.487140E-01 14.0000 0.486811E-18 0.294021E-02 0.171471E-01 0.434296E-01 16.0000 0.277304E-16 0.275223E-02 0.149957E-01 0.393141E-01 18.0000 0.737079E-15 0.259623E-02 0.133889E-01 0.360067E-01 20.0000 0.110878E-13 0.246407E-02 0.120253E-01 0.332831E-01 Expected final conditions: 20.0000 0.189133E-13 0.246589E-02 0.120455E-01 0.333141E-01 EULER_TEST Problem number = 15 Problem p15, Enright and Pryce #C5 The system is autonomous. Number of equations is 30 The system is large. Print only MIN, AVERAGE, MAX, L2NORM Stepsize H = 0.400000E-01 0.00000 -30.1552 1.67452 28.4465 53.8448 2.00000 -30.1971 1.60076 28.0107 53.7352 4.00000 -30.2263 1.49385 27.5686 53.6276 6.00000 -30.2427 1.35809 27.1204 53.5215 8.00000 -30.2460 1.19929 26.6659 53.4167 10.0000 -30.2362 1.02404 26.2054 53.3126 12.0000 -30.2133 0.839106 25.7389 53.2088 14.0000 -30.1771 0.650979 25.2665 53.1051 16.0000 -30.1277 0.465574 24.7883 53.0010 18.0000 -30.0650 0.288037 24.3045 52.8965 20.0000 -29.9891 0.122618 23.8152 52.7913 Expected final conditions: 20.0000 -29.9876 0.126877 23.8146 52.7668 EULER_TEST Problem number = 16 Problem p16, Enright and Pryce #D1 The system is autonomous. Number of equations is 4 Stepsize H = 0.400000E-01 0.00000 0.900000 0.00000 0.00000 1.10554 2.00000 -0.586227 1.00961 -0.887472 -0.314702 4.00000 -1.42748 -0.307350 0.864292E-01 -0.765272 6.00000 -0.517198 -1.40489 0.736555 -0.214687 8.00000 0.954248 -0.938356 0.545718 0.697838 10.0000 0.999287 0.805188 -0.559590 0.773256 12.0000 -0.590537 1.43195 -0.814484 -0.159596 14.0000 -1.77898 0.564467 -0.327949 -0.616122 16.0000 -1.92098 -0.715580 0.178915 -0.607343 18.0000 -1.17616 -1.69302 0.543898 -0.327864 20.0000 0.958354E-01 -1.91392 0.682299 0.143165 Expected final conditions: 20.0000 0.219884 0.942708 -0.978766 0.328798 EULER_TEST Problem number = 17 Problem p17, Enright and Pryce #D2 The system is autonomous. Number of equations is 4 Stepsize H = 0.400000E-01 0.00000 0.700000 0.00000 0.00000 1.36277 2.00000 -0.961448 0.988229 -0.795780 -0.287437 4.00000 -1.87125 0.895048E-02 -0.130991 -0.577877 6.00000 -1.61666 -1.05240 0.375901 -0.432356 8.00000 -0.464973 -1.51373 0.750832 0.567084E-01 10.0000 0.920125 -0.416680 0.296045 1.12337 12.0000 -0.945220E-01 1.39202 -0.910507 0.339105 14.0000 -1.67060 1.38577 -0.625287 -0.232313 16.0000 -2.62234 0.736282 -0.332055 -0.387838 18.0000 -3.04814 -0.817735E-01 -0.964640E-01 -0.417824 20.0000 -3.03912 -0.895068 0.105537 -0.386481 Expected final conditions: 20.0000 -0.177703 0.946778 -1.03029 0.121107 EULER_TEST Problem number = 18 Problem p18, Enright and Pryce #D3 The system is autonomous. Number of equations is 4 Stepsize H = 0.400000E-01 0.00000 0.500000 0.00000 0.00000 1.73205 2.00000 -1.38210 1.04791 -0.793315 -0.129720 4.00000 -2.54968 0.558469 -0.406474 -0.310582 6.00000 -3.11332 -0.964694E-01 -0.165686 -0.333513 8.00000 -3.25504 -0.745671 0.225306E-01 -0.309657 10.0000 -3.04261 -1.31621 0.191974 -0.254471 12.0000 -2.49322 -1.74078 0.362512 -0.159791 14.0000 -1.58653 -1.90982 0.552993 0.143766E-01 16.0000 -0.270893 -1.53328 0.761443 0.456658 18.0000 0.542711 0.592226 -0.768091 1.30650 20.0000 -1.33773 1.76989 -0.848222 0.214875 Expected final conditions: 20.0000 -0.578043 0.863384 -0.959508 -0.650492E-01 EULER_TEST Problem number = 19 Problem p19, Enright and Pryce #D4 The system is autonomous. Number of equations is 4 Stepsize H = 0.400000E-01 0.00000 0.300000 0.00000 0.00000 2.38048 2.00000 -2.12141 1.50127 -1.06372 0.308275 4.00000 -4.08206 2.01301 -0.918754 0.221597 6.00000 -5.85080 2.42416 -0.855387 0.192829 8.00000 -7.52276 2.79430 -0.818649 0.178385 10.0000 -9.13472 3.14188 -0.794290 0.169666 12.0000 -10.7053 3.47513 -0.776801 0.163817 14.0000 -12.2453 3.79844 -0.763561 0.159613 16.0000 -13.7619 4.11442 -0.753151 0.156441 18.0000 -15.2596 4.42477 -0.744729 0.153960 20.0000 -16.7421 4.73067 -0.737762 0.151965 Expected final conditions: 20.0000 -0.953899 0.690741 -0.821267 -0.153957 EULER_TEST Problem number = 20 Problem p20, Enright and Pryce #D5 The system is autonomous. Number of equations is 4 Stepsize H = 0.400000E-01 0.00000 0.100000 0.00000 0.00000 4.35890 2.00000 -8.18069 5.92136 -4.18834 2.85647 4.00000 -16.5476 11.6273 -4.18025 2.85070 6.00000 -24.9051 17.3266 -4.17756 2.84882 8.00000 -33.2588 23.0232 -4.17621 2.84788 10.0000 -41.6103 28.7184 -4.17540 2.84733 12.0000 -49.9606 34.4127 -4.17486 2.84695 14.0000 -58.3099 40.1063 -4.17448 2.84669 16.0000 -66.6586 45.7995 -4.17419 2.84649 18.0000 -75.0067 51.4923 -4.17397 2.84634 20.0000 -83.3545 57.1849 -4.17379 2.84621 Expected final conditions: 20.0000 -1.29527 0.400394 -0.677539 -0.127084 EULER_TEST Problem number = 21 Problem p21, Enright and Pryce #E1 The system is autonomous. Number of equations is 2 Stepsize H = 0.400000E-01 0.00000 0.671397 0.954005E-01 2.00000 0.618914E-01 -0.480441 4.00000 -0.363253 0.151809 6.00000 0.226359 0.230530 8.00000 0.118283 -0.290063 10.0000 -0.288875 0.238092E-01 12.0000 0.124902 0.242082 14.0000 0.166758 -0.215429 16.0000 -0.254471 -0.549949E-01 18.0000 0.486060E-01 0.252045 20.0000 0.207866 -0.153260 Expected final conditions: 20.0000 0.145672 -0.988350E-01 EULER_TEST Problem number = 22 Problem p22, Enright and Pryce #E2 The system is autonomous. Number of equations is 2 Stepsize H = 0.400000E-01 0.00000 2.00000 0.00000 2.00000 0.365057 -1.78274 4.00000 -1.82354 0.615083 6.00000 0.933563 2.73191 8.00000 1.41878 -0.856738 10.0000 -2.02372 -0.593265 12.0000 -0.835665 1.31149 14.0000 1.99233 -0.463725 16.0000 -0.131546 -2.30436 18.0000 -1.66138 0.712237 20.0000 1.56934 2.13116 Expected final conditions: 20.0000 2.00815 -0.425089E-01 EULER_TEST Problem number = 23 Problem p23, Enright and Pryce #E3 The system is autonomous. Number of equations is 2 Stepsize H = 0.400000E-01 0.00000 0.00000 0.00000 2.00000 1.07621 -0.741100 4.00000 -0.162926 -0.815062 6.00000 -0.484191 1.07074 8.00000 0.903669 1.24688 10.0000 0.201687 -0.208941 12.0000 -1.37661 0.161353 14.0000 -0.148877 0.826544 16.0000 1.12810 -0.911859 18.0000 -0.545263 -1.91517 20.0000 -1.12685 0.123699 Expected final conditions: 20.0000 -0.100418 0.241140 EULER_TEST Problem number = 24 Problem p24, Enright and Pryce #E4 The system is autonomous. Number of equations is 2 Stepsize H = 0.400000E-01 0.00000 30.0000 0.00000 2.00000 30.0622 0.629604E-01 4.00000 30.2455 0.120027 6.00000 30.5336 0.167269 8.00000 30.9055 0.203524 10.0000 31.3398 0.229759 12.0000 31.8183 0.247944 14.0000 32.3270 0.260177 16.0000 32.8558 0.268242 18.0000 33.3978 0.273486 20.0000 33.9483 0.276868 Expected final conditions: 20.0000 33.9509 0.276782 EULER_TEST Problem number = 25 Problem p25, Enright and Pryce #E5 The system is not autonomous. Number of equations is 2 Stepsize H = 0.400000E-01 0.00000 0.00000 0.00000 2.00000 0.805329E-01 0.834056E-01 4.00000 0.335611 0.175070 6.00000 0.784145 0.277596 8.00000 1.45135 0.394809 10.0000 2.37191 0.532570 12.0000 3.59538 0.700335 14.0000 5.19620 0.914412 16.0000 7.29362 1.20554 18.0000 10.0971 1.63940 20.0000 14.0291 2.38591 Expected final conditions: 20.0000 14.1180 2.40000 EULER_TEST Problem number = 26 Problem p26, Enright and Pryce #F1 The system is autonomous. Number of equations is 2 Stepsize H = 0.400000E-01 0.00000 0.00000 0.00000 2.00000 -0.555314 -0.574070E-01 4.00000 -1.55359 -0.340860 6.00000 -3.34225 -1.17388 8.00000 -6.53639 -3.24993 10.0000 -12.2210 -8.01326 12.0000 -22.3028 -18.4082 14.0000 -40.1192 -40.3377 16.0000 -71.4867 -85.4795 18.0000 -126.498 -176.679 20.0000 -222.577 -358.211 Expected final conditions: 20.0000 -12.9446 -0.220858E-14 EULER_TEST Problem number = 27 Problem p27, Enright and Pryce #F2 The system is not autonomous. Number of equations is 1 Stepsize H = 0.400000E-01 0.00000 110.000 2.00000 75.1681 4.00000 70.6927 6.00000 70.1177 8.00000 70.0438 10.0000 70.0343 12.0000 70.0331 14.0000 70.0330 16.0000 70.0329 18.0000 70.0329 20.0000 70.0329 Expected final conditions: 20.0000 70.0373 EULER_TEST Problem number = 28 Problem p28, Enright and Pryce #F3 The system is autonomous. Number of equations is 2 Stepsize H = 0.400000E-01 0.00000 0.00000 0.00000 2.00000 -0.918705 -0.636069 4.00000 -1.11864 0.512064 6.00000 0.587152E-01 0.210702 8.00000 -0.743514 -0.784145 10.0000 -1.33428 0.411146 12.0000 0.541261E-01 0.459671 14.0000 -0.503562 -0.887968 16.0000 -1.53699 0.231113 18.0000 -0.323236E-01 0.729106 20.0000 -0.207811 -0.921752 Expected final conditions: 20.0000 -0.372696 -0.623014 EULER_TEST Problem number = 29 Problem p29, Enright and Pryce #F4 The system is not autonomous. Number of equations is 1 Stepsize H = 0.400000E-01 0.00000 1.00000 2.00000 15.7970 4.00000 45.3449 6.00000 46.1144 8.00000 15.6148 10.0000 0.285243 12.0000 0.736499E-03 14.0000 0.113910E-04 16.0000 0.176179E-06 18.0000 0.272487E-08 20.0000 0.421442E-10 Expected final conditions: 20.0000 0.981502E-10 EULER_TEST Problem number = 30 Problem p30, Enright and Pryce #F5 The system is not autonomous. Number of equations is 1 Stepsize H = 0.400000E-01 0.00000 1.00000 2.00000 0.801068 4.00000 0.671236 6.00000 0.590582 8.00000 0.546518 10.0000 0.532350 12.0000 0.545947 14.0000 0.589292 16.0000 0.668885 18.0000 0.797008 20.0000 0.993199 Expected final conditions: 20.0000 1.00000 EULER_TEST Problem number = 31 Problem p31, Lotka-Volterra Predator-Prey Equations. The system is autonomous. Number of equations is 2 Stepsize H = 0.200000E-01 0.00000 2.00000 2.00000 1.00000 4.62061 11.7729 2.00000 0.650036 2.50530 3.00000 15.3994 3.38015 4.00000 0.167532 4.80844 5.00000 2.51121 0.879755 6.00000 0.641051 15.2104 7.00000 0.841158E-01 2.08900 8.00000 4.08332 0.432882 9.00000 0.379692E-01 14.6164 10.0000 0.817064E-02 1.90613 Expected final conditions: 10.0000 2.20050 10.2726 EULER_TEST Problem number = 33 Problem p33, The Van der Pol equation The system is autonomous. Number of equations is 2 Stepsize H = 0.400000E-01 0.00000 2.00000 2.00000 2.00000 1.43713 -0.857275 4.00000 -2.01527 -0.653273 6.00000 -0.857082 1.29183 8.00000 1.99979 -0.452663 10.0000 -0.939778E-01 -2.26809 12.0000 -1.67312 0.705521 14.0000 1.53160 2.20414 16.0000 1.20808 -1.00101 18.0000 -2.08675 0.839823E-01 20.0000 -0.503607 1.64126 Expected final conditions: 20.0000 0.756245 2.67294 EULER_TEST Problem number = 34 Problem p34, The Linearized Damped Pendulum The system is autonomous. Number of equations is 2 Stepsize H = 0.400000E-01 0.00000 2.00000 2.00000 2.00000 0.128779 15.3247 4.00000 -3.38754 8.75688 6.00000 -2.93203 -19.7468 8.00000 3.56880 -31.0642 10.0000 7.96922 9.63661 12.0000 0.140522 61.9157 14.0000 -13.7958 32.6642 16.0000 -11.2707 -81.9524 18.0000 15.0695 -122.502 20.0000 31.7134 45.1238 Expected final conditions: 20.0000 0.695786E-04 0.277616E-03 EULER_TEST Problem number = 35 Problem p35, The Nonlinear Damped Pendulum The system is autonomous. Number of equations is 2 Stepsize H = 0.400000E-01 0.00000 2.00000 2.00000 2.00000 -0.936744 -6.35046 4.00000 0.982658 5.35377 6.00000 -1.25883 -3.06297 8.00000 1.42479 0.142207 10.0000 -1.33254 2.85870 12.0000 0.940379 -5.55191 14.0000 -0.283944 7.15841 16.0000 -0.483769 -6.51797 18.0000 1.10431 3.69474 20.0000 -1.38411 -0.154747 Expected final conditions: 20.0000 -0.584253E-04 0.359969E-03 EULER_TEST Problem number = 38 Problem p38, Shampine's Ball of Flame The system is autonomous. Number of equations is 1 Stepsize H = 0.400000 0.00000 0.100000E-01 20.0000 0.124519E-01 40.0000 0.164735E-01 60.0000 0.242423E-01 80.0000 0.451724E-01 100.000 0.221404 120.000 1.00000 140.000 1.00000 160.000 1.00000 180.000 1.00000 200.000 1.00000 Expected final conditions: 200.000 1.00000 EULER_TEST Problem number = 39 Problem p39, Polking's first order ODE The system is not autonomous. Number of equations is 1 Stepsize H = 0.180000E-01 0.00000 0.500000 0.900000 0.323498 1.80000 -0.762258 2.70000 -1.49097 3.60000 -1.81767 4.50000 -2.06138 5.40000 -2.27490 6.30000 -2.46859 7.20000 -2.64736 8.10000 -2.81431 9.00000 -2.97156 Expected final conditions: 9.00000 -3.00000 EULER_TEST Problem number = 40 Problem p40, the Knee problem The system is not autonomous. Number of equations is 1 Stepsize H = 0.400000E-02 -1.00000 -1.00000 -0.800000 -0.812136 -0.600000 -0.615846 -0.400000 -0.422554 -0.200000 -0.237288 0.00000 -0.796024E-01 0.200000 -0.525767E-02 0.400000 -0.884221E-05 0.600000 -0.129933E-09 0.800000 -0.984709E-17 1.00000 -0.206690E-26 Expected final conditions: 1.00000 -0.915216E-23 TEST03 Solve problems using a Runge-Kutta method. The number of steps taken is 500 The number of tests available is 40 RK_TEST Problem number = 1 Runge Kutta order = 3 Problem p01, Enright and Pryce #A1, exponential decay. The system is autonomous. Number of equations is 1 Stepsize H = 0.400000E-01 0.00000 1.00000 2.00000 0.135335 4.00000 0.183154E-01 6.00000 0.247871E-02 8.00000 0.335455E-03 10.0000 0.453987E-04 12.0000 0.614401E-05 14.0000 0.831497E-06 16.0000 0.112530E-06 18.0000 0.152292E-07 20.0000 0.206104E-08 Expected final conditions: 20.0000 0.206115E-08 RK_TEST Problem number = 2 Runge Kutta order = 3 Problem p02, Enright and Pryce #A2 The system is autonomous. Number of equations is 1 Stepsize H = 0.400000E-01 0.00000 1.00000 2.00000 0.577350 4.00000 0.447214 6.00000 0.377964 8.00000 0.333333 10.0000 0.301511 12.0000 0.277350 14.0000 0.258199 16.0000 0.242536 18.0000 0.229416 20.0000 0.218218 Expected final conditions: 20.0000 0.218218 RK_TEST Problem number = 3 Runge Kutta order = 3 Problem p03, Enright and Pryce #A3 The system is not autonomous. Number of equations is 1 Stepsize H = 0.400000E-01 0.00000 1.00000 2.00000 2.48258 4.00000 0.469164 6.00000 0.756228 8.00000 2.68952 10.0000 0.580411 12.0000 0.584752 14.0000 2.69288 16.0000 0.749837 18.0000 0.471904 20.0000 2.49166 Expected final conditions: 20.0000 2.49165 RK_TEST Problem number = 4 Runge Kutta order = 3 Problem p04, Enright and Pryce #A4 The system is autonomous. Number of equations is 1 Stepsize H = 0.400000E-01 0.00000 1.00000 2.00000 1.59692 4.00000 2.50322 6.00000 3.81718 8.00000 5.60009 10.0000 7.81367 12.0000 10.2777 14.0000 12.7085 16.0000 14.8368 18.0000 16.5143 20.0000 17.7302 Expected final conditions: 20.0000 17.7302 RK_TEST Problem number = 5 Runge Kutta order = 3 Problem p05, Enright and Pryce #A5 The system is not autonomous. Number of equations is 1 Stepsize H = 0.400000E-01 0.00000 4.00000 2.00000 5.35684 4.00000 5.99311 6.00000 6.20185 8.00000 6.07875 10.0000 5.66431 12.0000 4.97366 14.0000 4.00586 16.0000 2.74625 18.0000 1.16494 20.0000 -0.788783 Expected final conditions: 20.0000 -0.788783 RK_TEST Problem number = 6 Runge Kutta order = 3 Problem p06, Enright and Pryce #B1 The system is autonomous. Number of equations is 2 Stepsize H = 0.400000E-01 0.00000 1.00000 3.00000 2.00000 0.849612E-01 0.577949 4.00000 1.44636 0.187187 6.00000 0.175577 2.25893 8.00000 0.147120 0.366734 10.0000 3.14291 0.348408 12.0000 0.756721E-01 1.43338 14.0000 0.300981 0.245158 16.0000 3.96342 1.54160 18.0000 0.655187E-01 0.889725 20.0000 0.674238 0.186039 Expected final conditions: 20.0000 0.676188 0.186082 RK_TEST Problem number = 7 Runge Kutta order = 3 Problem p07, Enright and Pryce #B2 The system is autonomous. Number of equations is 3 Stepsize H = 0.400000E-01 0.00000 2.00000 0.00000 1.00000 2.00000 1.06891 0.997522 0.933572 4.00000 1.00916 0.999994 0.990845 6.00000 1.00124 1.00000 0.998761 8.00000 1.00017 1.00000 0.999832 10.0000 1.00002 1.00000 0.999977 12.0000 1.00000 1.00000 0.999997 14.0000 1.00000 1.00000 1.00000 16.0000 1.00000 1.00000 1.00000 18.0000 1.00000 1.00000 1.00000 20.0000 1.00000 1.00000 1.00000 Expected final conditions: 20.0000 1.00000 1.00000 1.00000 RK_TEST Problem number = 8 Runge Kutta order = 3 Problem p08, Enright and Pryce #B3 The system is autonomous. Number of equations is 3 Stepsize H = 0.400000E-01 0.00000 1.00000 0.00000 0.00000 2.00000 0.135335 0.478424 0.386242 4.00000 0.183154E-01 0.297188 0.684496 6.00000 0.247871E-02 0.195491 0.802030 8.00000 0.335455E-03 0.141977 0.857688 10.0000 0.453987E-04 0.110791 0.889164 12.0000 0.614401E-05 0.907250E-01 0.909269 14.0000 0.831497E-06 0.767955E-01 0.923204 16.0000 0.112530E-06 0.665714E-01 0.933428 18.0000 0.152292E-07 0.587494E-01 0.941251 20.0000 0.206104E-08 0.525723E-01 0.947428 Expected final conditions: 20.0000 0.206115E-08 0.525723E-01 0.947428 RK_TEST Problem number = 9 Runge Kutta order = 3 Problem p09, Enright and Pryce #B4 The system is autonomous. Number of equations is 3 Stepsize H = 0.400000E-01 0.00000 3.00000 0.00000 0.00000 2.00000 -0.659103 1.44019 0.909296 4.00000 -0.880038 -1.01891 -0.756803 6.00000 2.84225 -0.827116 -0.279418 8.00000 -0.269818 1.83475 0.989354 10.0000 -0.974092 -0.631551 -0.544022 12.0000 2.39978 -1.52593 -0.536578 14.0000 0.292178 2.11664 0.990601 16.0000 -0.998195 -0.300078 -0.287905 18.0000 1.75664 -1.99786 -0.750995 20.0000 0.982699 2.19843 0.912937 Expected final conditions: 20.0000 0.982695 2.19845 0.912945 RK_TEST Problem number = 10 Runge Kutta order = 3 Problem p10, Enright and Pryce #B5 The system is autonomous. Number of equations is 3 Stepsize H = 0.400000E-01 0.00000 0.00000 1.00000 1.00000 2.00000 0.995363 -0.961557E-01 0.703360 4.00000 -0.269604 -0.962965 0.981287 6.00000 -0.957499 0.288404 0.729672 8.00000 0.510895 0.859628 0.931060 10.0000 0.877890 -0.478832 0.779060 12.0000 -0.705371 -0.708811 0.863848 14.0000 -0.750432 0.660916 0.844260 16.0000 0.847241 0.531161 0.796173 18.0000 0.570605 -0.821191 0.913195 20.0000 -0.939613 -0.342146 0.741423 Expected final conditions: 20.0000 -0.939657 -0.342118 0.741413 RK_TEST Problem number = 11 Runge Kutta order = 3 Problem p11, Enright and Pryce #C1 The system is autonomous. Number of equations is 10 The system is large. Print only MIN, AVERAGE, MAX, L2NORM Stepsize H = 0.400000E-01 0.00000 0.00000 0.100000 1.00000 1.00000 2.00000 0.237398E-03 0.100000 0.270672 0.454975 4.00000 0.183154E-01 0.100000 0.195367 0.379053 6.00000 0.247871E-02 0.100000 0.160623 0.364212 8.00000 0.335455E-03 0.100000 0.407453 0.482198 10.0000 0.453987E-04 0.100000 0.667180 0.686841 12.0000 0.614401E-05 0.100000 0.844972 0.849130 14.0000 0.831497E-06 0.100000 0.937945 0.938648 16.0000 0.112530E-06 0.100000 0.978013 0.978109 18.0000 0.152292E-07 0.100000 0.992944 0.992955 20.0000 0.206104E-08 0.100000 0.997913 0.997914 Expected final conditions: 20.0000 0.206115E-08 0.100000 0.997913 0.997914 RK_TEST Problem number = 12 Runge Kutta order = 3 Problem p12, Enright and Pryce #C2 The system is autonomous. Number of equations is 10 The system is large. Print only MIN, AVERAGE, MAX, L2NORM Stepsize H = 0.400000E-01 0.00000 0.00000 0.100000 1.00000 1.00000 2.00000 0.422845E-01 0.100000 0.270164 0.374527 4.00000 0.157980E-01 0.100000 0.846734 0.848277 6.00000 0.242999E-02 0.100000 0.977911 0.977939 8.00000 0.334556E-03 0.100000 0.996985 0.996985 10.0000 0.453822E-04 0.100000 0.999591 0.999591 12.0000 0.614371E-05 0.100000 0.999945 0.999945 14.0000 0.831491E-06 0.100000 0.999993 0.999993 16.0000 0.112530E-06 0.100000 0.999999 0.999999 18.0000 0.152292E-07 0.100000 1.00000 1.00000 20.0000 0.206104E-08 0.100000 1.00000 1.00000 Expected final conditions: 20.0000 0.206115E-08 0.100000 1.00000 1.00000 RK_TEST Problem number = 13 Runge Kutta order = 3 Problem p13, Enright and Pryce #C3 The system is autonomous. Number of equations is 10 The system is large. Print only MIN, AVERAGE, MAX, L2NORM Stepsize H = 0.400000E-01 0.00000 0.00000 0.100000 1.00000 1.00000 2.00000 0.357044E-04 0.385742E-01 0.117627 0.183127 4.00000 0.845855E-03 0.276900E-01 0.593958E-01 0.110308 6.00000 0.248790E-02 0.223908E-01 0.394235E-01 0.816235E-01 8.00000 0.375884E-02 0.187544E-01 0.300609E-01 0.654230E-01 10.0000 0.430091E-02 0.158770E-01 0.237901E-01 0.542966E-01 12.0000 0.430786E-02 0.134840E-01 0.197607E-01 0.457271E-01 14.0000 0.402510E-02 0.114625E-01 0.166272E-01 0.387385E-01 16.0000 0.361899E-02 0.974673E-02 0.140406E-01 0.328947E-01 18.0000 0.318260E-02 0.828850E-02 0.118864E-01 0.279579E-01 20.0000 0.276243E-02 0.704861E-02 0.100794E-01 0.237705E-01 Expected final conditions: 20.0000 0.276243E-02 0.704861E-02 0.100794E-01 0.237705E-01 RK_TEST Problem number = 14 Runge Kutta order = 3 Problem p14, Enright and Pryce #C4 The system is autonomous. Number of equations is 51 The system is large. Print only MIN, AVERAGE, MAX, L2NORM Stepsize H = 0.400000E-01 0.00000 0.00000 0.196078E-01 1.00000 1.00000 2.00000 0.347735E-51 0.756377E-02 0.117627 0.183127 4.00000 0.173176E-37 0.544263E-02 0.593958E-01 0.110312 6.00000 0.314113E-30 0.446844E-02 0.394240E-01 0.817232E-01 8.00000 0.173091E-25 0.388027E-02 0.300773E-01 0.659967E-01 10.0000 0.431636E-22 0.347621E-02 0.238558E-01 0.558938E-01 12.0000 0.159849E-19 0.317671E-02 0.200765E-01 0.487893E-01 14.0000 0.164897E-17 0.294330E-02 0.171883E-01 0.434872E-01 16.0000 0.687593E-16 0.275477E-02 0.150185E-01 0.393598E-01 18.0000 0.146997E-14 0.259836E-02 0.134107E-01 0.360439E-01 20.0000 0.189122E-13 0.246589E-02 0.120455E-01 0.333141E-01 Expected final conditions: 20.0000 0.189133E-13 0.246589E-02 0.120455E-01 0.333141E-01 RK_TEST Problem number = 15 Runge Kutta order = 3 Problem p15, Enright and Pryce #C5 The system is autonomous. Number of equations is 30 The system is large. Print only MIN, AVERAGE, MAX, L2NORM Stepsize H = 0.400000E-01 0.00000 -30.1552 1.67452 28.4465 53.8448 2.00000 -30.1970 1.60039 28.0106 53.7343 4.00000 -30.2261 1.49310 27.5685 53.6255 6.00000 -30.2423 1.35693 27.1202 53.5181 8.00000 -30.2455 1.19771 26.6657 53.4116 10.0000 -30.2356 1.02211 26.2051 53.3054 12.0000 -30.2125 0.837004 25.7385 53.1990 14.0000 -30.1761 0.649100 25.2660 53.0922 16.0000 -30.1265 0.464601 24.7878 52.9847 18.0000 -30.0637 0.288995 24.3039 52.8762 20.0000 -29.9876 0.126877 23.8146 52.7668 Expected final conditions: 20.0000 -29.9876 0.126877 23.8146 52.7668 RK_TEST Problem number = 16 Runge Kutta order = 3 Problem p16, Enright and Pryce #D1 The system is autonomous. Number of equations is 4 Stepsize H = 0.400000E-01 0.00000 0.900000 0.00000 0.00000 1.10554 2.00000 -0.593536 0.865347 -0.828796 -0.468003 4.00000 -0.805444 -0.705108 0.662051 -0.655724 6.00000 0.851156 -0.307012 0.341025 1.04594 8.00000 -0.341132 0.965534 -0.947651 -0.234365 10.0000 -0.964691 -0.499433 0.462129 -0.792097 12.0000 0.711845 -0.580772 0.635397 0.879264 14.0000 -0.644458E-01 0.994210 -1.00299 0.354173E-01 16.0000 -1.06404 -0.263340 0.241510 -0.875244 18.0000 0.500642 -0.795298 0.850643 0.635929 20.0000 0.216372 0.943681 -0.979714 0.325050 Expected final conditions: 20.0000 0.219884 0.942708 -0.978766 0.328798 RK_TEST Problem number = 17 Runge Kutta order = 3 Problem p17, Enright and Pryce #D2 The system is autonomous. Number of equations is 4 Stepsize H = 0.400000E-01 0.00000 0.700000 0.00000 0.00000 1.36277 2.00000 -0.917180 0.750470 -0.663793 -0.496907 4.00000 -1.08230 -0.593865 0.504361 -0.604625 6.00000 0.621567 -0.370244 0.536506 1.21508 8.00000 -0.708560 0.870357 -0.812958 -0.347583 10.0000 -1.20071 -0.413049 0.341108 -0.677057 12.0000 0.416811 -0.664979 0.888362 0.871117 14.0000 -0.462351 0.940858 -0.940902 -0.148222 16.0000 -1.27257 -0.217616 0.176804 -0.719261 18.0000 0.145419 -0.853765 1.03364 0.490249 20.0000 -0.187388 0.947432 -1.02852 0.110626 Expected final conditions: 20.0000 -0.177703 0.946778 -1.03029 0.121107 RK_TEST Problem number = 18 Runge Kutta order = 3 Problem p18, Enright and Pryce #D3 The system is autonomous. Number of equations is 4 Stepsize H = 0.400000E-01 0.00000 0.500000 0.00000 0.00000 1.73205 2.00000 -1.20533 0.613050 -0.523259 -0.452281 4.00000 -1.33223 -0.478108 0.390362 -0.509893 6.00000 0.362725 -0.437726 0.889397 1.31391 8.00000 -1.04110 0.726054 -0.660414 -0.370996 10.0000 -1.41816 -0.334813 0.265730 -0.547732 12.0000 0.825121E-01 -0.703309 1.14752 0.711051 14.0000 -0.847935 0.809140 -0.797236 -0.260013 16.0000 -1.46907 -0.190072 0.148611 -0.569954 18.0000 -0.207504 -0.826691 1.12094 0.294569 20.0000 -0.629457 0.855939 -0.930547 -0.109409 Expected final conditions: 20.0000 -0.578043 0.863384 -0.959508 -0.650492E-01 RK_TEST Problem number = 19 Runge Kutta order = 3 Problem p19, Enright and Pryce #D4 The system is autonomous. Number of equations is 4 Stepsize H = 0.400000E-01 0.00000 0.300000 0.00000 0.00000 2.38048 2.00000 -1.46131 0.448709 -0.407981 -0.362966 4.00000 -1.53336 -0.367842 0.330392 -0.386039 6.00000 0.145851 -0.379406 1.31140 1.47989 8.00000 -1.36610 0.492001 -0.470864 -0.351702 10.0000 -1.51405 -0.337514 0.310492 -0.401131 12.0000 0.154367 -0.368227 1.29967 1.51245 14.0000 -1.35807 0.466579 -0.450672 -0.368541 16.0000 -1.43325 -0.382817 0.369512 -0.397226 18.0000 0.299584 0.245121E-01 -0.110228 2.36109 20.0000 -1.42113 0.366942 -0.344461 -0.410257 Expected final conditions: 20.0000 -0.953899 0.690741 -0.821267 -0.153957 RK_TEST Problem number = 20 Runge Kutta order = 3 Problem p20, Enright and Pryce #D5 The system is autonomous. Number of equations is 4 Stepsize H = 0.400000E-01 0.00000 0.100000 0.00000 0.00000 4.35890 2.00000 -2.34833 1.97369 -1.01672 0.672361 4.00000 -4.27075 3.22859 -0.922390 0.597144 6.00000 -6.07118 4.38987 -0.882398 0.567575 8.00000 -7.81147 5.50745 -0.859692 0.551362 10.0000 -9.51512 6.59915 -0.844891 0.541012 12.0000 -11.1939 7.67356 -0.834417 0.533790 14.0000 -12.8545 8.73555 -0.826587 0.528446 16.0000 -14.5014 9.78815 -0.820498 0.524322 18.0000 -16.1373 10.8334 -0.815620 0.521038 20.0000 -17.7644 11.8727 -0.811619 0.518358 Expected final conditions: 20.0000 -1.29527 0.400394 -0.677539 -0.127084 RK_TEST Problem number = 21 Runge Kutta order = 3 Problem p21, Enright and Pryce #E1 The system is autonomous. Number of equations is 2 Stepsize H = 0.400000E-01 0.00000 0.671397 0.954005E-01 2.00000 0.650098E-01 -0.466882 4.00000 -0.342166 0.135431 6.00000 0.198125 0.213203 8.00000 0.109608 -0.248410 10.0000 -0.240564 0.119970E-01 12.0000 0.929755E-01 0.197231 14.0000 0.133965 -0.160964 16.0000 -0.186038 -0.477768E-01 18.0000 0.274312E-01 0.180250 20.0000 0.145666 -0.988284E-01 Expected final conditions: 20.0000 0.145672 -0.988350E-01 RK_TEST Problem number = 22 Runge Kutta order = 3 Problem p22, Enright and Pryce #E2 The system is autonomous. Number of equations is 2 Stepsize H = 0.400000E-01 0.00000 2.00000 0.00000 2.00000 0.323315 -1.83298 4.00000 -1.74174 0.624686 6.00000 1.27913 2.43768 8.00000 1.21316 -0.987873 10.0000 -2.00832 0.330649E-01 12.0000 -0.313559 1.84425 14.0000 1.73855 -0.627227 16.0000 -1.29175 -2.42279 18.0000 -1.20803 0.991760 20.0000 2.00812 -0.428777E-01 Expected final conditions: 20.0000 2.00815 -0.425089E-01 RK_TEST Problem number = 23 Runge Kutta order = 3 Problem p23, Enright and Pryce #E3 The system is autonomous. Number of equations is 2 Stepsize H = 0.400000E-01 0.00000 0.00000 0.00000 2.00000 1.01302 -0.809881 4.00000 -0.177324 -0.797716 6.00000 -0.336553 1.02634 8.00000 0.862209 1.09893 10.0000 0.305900E-01 -0.640955E-01 12.0000 -1.12098 0.414704 14.0000 0.551310E-01 0.539507 16.0000 0.538173 -1.15982 18.0000 -0.680319 -1.26679 20.0000 -0.100417 0.241133 Expected final conditions: 20.0000 -0.100418 0.241140 RK_TEST Problem number = 24 Runge Kutta order = 3 Problem p24, Enright and Pryce #E4 The system is autonomous. Number of equations is 2 Stepsize H = 0.400000E-01 0.00000 30.0000 0.00000 2.00000 30.0635 0.629296E-01 4.00000 30.2477 0.119923 6.00000 30.5365 0.167090 8.00000 30.9087 0.203299 10.0000 31.3431 0.229523 12.0000 31.8215 0.247727 14.0000 32.3300 0.259992 16.0000 32.8587 0.268093 18.0000 33.4005 0.273372 20.0000 33.9509 0.276782 Expected final conditions: 20.0000 33.9509 0.276782 RK_TEST Problem number = 25 Runge Kutta order = 3 Problem p25, Enright and Pryce #E5 The system is not autonomous. Number of equations is 2 Stepsize H = 0.400000E-01 0.00000 0.00000 0.00000 2.00000 0.822701E-01 0.834783E-01 4.00000 0.339417 0.175238 6.00000 0.790461 0.277895 8.00000 1.46078 0.395294 10.0000 2.38532 0.533333 12.0000 3.61408 0.701538 14.0000 5.22226 0.916364 16.0000 7.33064 1.20889 18.0000 10.1521 1.64571 20.0000 14.1180 2.40000 Expected final conditions: 20.0000 14.1180 2.40000 RK_TEST Problem number = 26 Runge Kutta order = 3 Problem p26, Enright and Pryce #F1 The system is autonomous. Number of equations is 2 Stepsize H = 0.400000E-01 0.00000 0.00000 0.00000 2.00000 -0.448455 0.281520E-01 4.00000 -0.995919 0.627214E-01 6.00000 -1.66425 0.105170 8.00000 -2.48014 0.157291 10.0000 -3.47615 0.221286 12.0000 -4.69206 0.299860 14.0000 -6.17643 0.396328 16.0000 -7.98850 0.514764 18.0000 -10.2006 0.660164 20.0000 -12.9012 0.838662 Expected final conditions: 20.0000 -12.9446 -0.220858E-14 RK_TEST Problem number = 27 Runge Kutta order = 3 Problem p27, Enright and Pryce #F2 The system is not autonomous. Number of equations is 1 Stepsize H = 0.400000E-01 0.00000 110.000 2.00000 75.1557 4.00000 70.4403 6.00000 69.8022 8.00000 69.7158 10.0000 69.7041 12.0000 69.7025 14.0000 69.7023 16.0000 69.7023 18.0000 69.7023 20.0000 69.7023 Expected final conditions: 20.0000 70.0373 RK_TEST Problem number = 28 Runge Kutta order = 3 Problem p28, Enright and Pryce #F3 The system is autonomous. Number of equations is 2 Stepsize H = 0.400000E-01 0.00000 0.00000 0.00000 2.00000 -0.922871 -0.593273 4.00000 -1.07307 0.495921 6.00000 -0.162338E-01 0.183719 8.00000 -0.747730 -0.655802 10.0000 -1.20315 0.363351 12.0000 -0.841808E-01 0.357691 14.0000 -0.559322 -0.666467 16.0000 -1.29230 0.197282 18.0000 -0.199765 0.507523 20.0000 -0.372714 -0.622981 Expected final conditions: 20.0000 -0.372696 -0.623014 RK_TEST Problem number = 29 Runge Kutta order = 3 Problem p29, Enright and Pryce #F4 The system is not autonomous. Number of equations is 1 Stepsize H = 0.400000E-01 0.00000 1.00000 2.00000 15.8726 4.00000 45.7043 6.00000 45.5138 8.00000 15.3011 10.0000 0.476190E-01 12.0000 0.144207E-03 14.0000 0.264100E-05 16.0000 0.483672E-07 18.0000 0.885795E-09 20.0000 0.162224E-10 Expected final conditions: 20.0000 0.981502E-10 RK_TEST Problem number = 30 Runge Kutta order = 3 Problem p30, Enright and Pryce #F5 The system is not autonomous. Number of equations is 1 Stepsize H = 0.400000E-01 0.00000 1.00000 2.00000 0.801762 4.00000 0.672347 6.00000 0.591952 8.00000 0.548099 10.0000 0.534169 12.0000 0.548099 14.0000 0.591952 16.0000 0.672347 18.0000 0.801762 20.0000 1.00000 Expected final conditions: 20.0000 1.00000 RK_TEST Problem number = 31 Runge Kutta order = 3 Problem p31, Lotka-Volterra Predator-Prey Equations. The system is autonomous. Number of equations is 2 Stepsize H = 0.200000E-01 0.00000 2.00000 2.00000 1.00000 4.27124 10.8258 2.00000 1.09884 2.63892 3.00000 11.4501 7.09808 4.00000 0.728731 3.72185 5.00000 10.6924 2.95016 6.00000 0.651837 5.37494 7.00000 5.83965 1.85974 8.00000 0.904342 7.70261 9.00000 2.87665 1.82161 10.0000 2.20051 10.2726 Expected final conditions: 10.0000 2.20050 10.2726 RK_TEST Problem number = 32 Runge Kutta order = 3 Problem p32, The Lorenz System The system is autonomous. Number of equations is 3 Stepsize H = 0.400000E-01 0.00000 2.00000 2.00000 21.0000 2.00000 -14.0607 -11.8529 36.5740 4.00000 -0.893976 -1.58277 13.9697 6.00000 7.33912 -0.535846 33.8690 8.00000 5.48819 9.49160 13.4183 10.0000 4.17926 1.53482 26.1721 12.0000 7.24339 13.6423 10.6864 14.0000 -3.57990 -5.88016 14.1580 16.0000 9.04477 4.21301 32.8742 18.0000 13.7897 10.6978 36.9939 20.0000 1.47355 2.53076 14.0202 Expected final conditions: 20.0000 0.00000 0.00000 0.00000 RK_TEST Problem number = 33 Runge Kutta order = 3 Problem p33, The Van der Pol equation The system is autonomous. Number of equations is 2 Stepsize H = 0.400000E-01 0.00000 2.00000 2.00000 2.00000 1.41596 -0.870930 4.00000 -1.96939 -0.504613 6.00000 -0.661781 1.47866 8.00000 1.85975 -0.518994 10.0000 -0.742405 -2.67077 12.0000 -1.40174 0.853029 14.0000 1.96521 0.504227 16.0000 0.654111 -1.48601 18.0000 -1.85702 0.521926 20.0000 0.756242 2.67294 Expected final conditions: 20.0000 0.756245 2.67294 RK_TEST Problem number = 34 Runge Kutta order = 3 Problem p34, The Linearized Damped Pendulum The system is autonomous. Number of equations is 2 Stepsize H = 0.400000E-01 0.00000 2.00000 2.00000 2.00000 0.963355E-02 4.26164 4.00000 -0.265830 0.572760 6.00000 -0.537171E-01 -0.457522 8.00000 0.249910E-01 -0.166906 10.0000 0.121196E-01 0.283286E-01 12.0000 -0.955163E-03 0.279298E-01 14.0000 -0.181077E-02 0.171618E-02 16.0000 -0.229261E-03 -0.340035E-02 18.0000 0.197183E-03 -0.900361E-03 20.0000 0.695787E-04 0.277616E-03 Expected final conditions: 20.0000 0.695786E-04 0.277616E-03 RK_TEST Problem number = 35 Runge Kutta order = 3 Problem p35, The Nonlinear Damped Pendulum The system is autonomous. Number of equations is 2 Stepsize H = 0.400000E-01 0.00000 2.00000 2.00000 2.00000 -0.711979 0.669499 4.00000 -0.510583E-01 -1.39731 6.00000 0.849338E-01 -0.274295 8.00000 0.228075E-01 0.134641 10.0000 -0.688752E-02 0.631099E-01 12.0000 -0.441003E-02 -0.558620E-02 14.0000 0.523152E-04 -0.954974E-02 16.0000 0.600664E-03 -0.113560E-02 18.0000 0.111461E-03 0.105441E-02 20.0000 -0.584252E-04 0.359969E-03 Expected final conditions: 20.0000 -0.584253E-04 0.359969E-03 RK_TEST Problem number = 36 Runge Kutta order = 3 Problem p36, Duffing's Equation The system is autonomous. Number of equations is 2 Stepsize H = 0.200000 0.00000 0.500000 0.00000 10.0000 0.524362 -0.106288 20.0000 0.567459 -0.193397 30.0000 0.616057 -0.260842 40.0000 0.660470 -0.308371 50.0000 0.694393 -0.337064 60.0000 0.714553 -0.348928 70.0000 0.720138 -0.345884 80.0000 0.712233 -0.329050 90.0000 0.693445 -0.298695 100.000 0.667713 -0.254718 Expected final conditions: 100.000 0.667726 -0.254738 RK_TEST Problem number = 37 Runge Kutta order = 3 Problem p37, Duffing's Equation with Damping and Forcing The system is not autonomous. Number of equations is 2 Stepsize H = 0.200000 0.00000 0.500000 0.00000 10.0000 -1.42987 -0.403663 20.0000 -0.674260 -0.333633 30.0000 -0.937308 0.322004 40.0000 -0.310489 -0.225079 50.0000 -0.853308 -0.594415 60.0000 -0.410462E-01 -0.200295 70.0000 0.973686E-01 0.584763 80.0000 -0.278932 -0.668705 90.0000 0.884018 0.792964 100.000 -1.17560 -0.586167 Expected final conditions: 100.000 -1.21774 -0.548248 RK_TEST Problem number = 38 Runge Kutta order = 3 Problem p38, Shampine's Ball of Flame The system is autonomous. Number of equations is 1 Stepsize H = 0.400000 0.00000 0.100000E-01 20.0000 0.124653E-01 40.0000 0.165265E-01 60.0000 0.244448E-01 80.0000 0.463580E-01 100.000 0.275572 120.000 1.00000 140.000 1.00000 160.000 1.00000 180.000 1.00000 200.000 1.00000 Expected final conditions: 200.000 1.00000 RK_TEST Problem number = 39 Runge Kutta order = 3 Problem p39, Polking's first order ODE The system is not autonomous. Number of equations is 1 Stepsize H = 0.180000E-01 0.00000 0.500000 0.900000 0.309665 1.80000 -0.774323 2.70000 -1.49024 3.60000 -1.81731 4.50000 -2.06128 5.40000 -2.27484 6.30000 -2.46855 7.20000 -2.64734 8.10000 -2.81429 9.00000 -2.97154 Expected final conditions: 9.00000 -3.00000 RK_TEST Problem number = 40 Runge Kutta order = 3 Problem p40, the Knee problem The system is not autonomous. Number of equations is 1 Stepsize H = 0.400000E-02 -1.00000 -1.00000 -0.800000 -0.812137 -0.600000 -0.615848 -0.400000 -0.422561 -0.200000 -0.237322 0.00000 -0.797884E-01 0.200000 -0.552465E-02 0.400000 -0.133753E-04 0.600000 -0.604638E-09 0.800000 -0.494403E-15 1.00000 -0.717575E-23 Expected final conditions: 1.00000 -0.915216E-23 TEST05 At a random time T in the time interval, and a random vector Y, compare the jacobian dF/dY and a finite difference estimate. The number of tests available is 40 Test Difference 1 0.171788E-09 2 0.718127E-08 3 0.197373E-08 4 0.307386E-08 5 0.00000 6 0.166806E-08 7 0.566790E-08 8 0.220514E-07 9 0.761029E-08 10 0.372946E-08 11 0.358786E-09 12 0.390557E-09 13 0.490515E-09 14 0.276843E-09 15 3.87371 16 0.188747E-06 17 0.214607E-06 18 0.929657E-07 19 0.499078E-07 20 0.365539E-07 21 0.297021E-09 22 0.403525E-08 23 0.136389E-08 24 0.715264E-08 25 0.159729E-08 26 0.192524E-06 27 0.750702E-08 28 0.275756E-08 29 0.00000 30 0.241685E-10 31 0.168546E-07 32 0.156892E-06 33 0.701863E-07 34 0.707587E-08 35 0.147085E-07 36 0.470444E-07 37 0.103800E-06 38 0.546645E-07 39 0.646321E-07 40 0.155562E-05 TEST_ODE_PRB Normal end of execution. 23 February 2013 12:37:19.786 PM