30-Mar-2019 18:15:23 test_ode_test MATLAB version Test test_ode. TEST01 List the problem titles and sizes. There are 40 test problems. Test Size Title 1 1 Problem 1, Enright and Pryce #A1, exponential decay. 2 1 Problem 2, Enright and Pryce #A2 3 1 Problem 3, Enright and Pryce #A3 4 1 Problem 4, Enright and Pryce #A4 5 1 Problem 5, Enright and Pryce #A5 6 2 Problem 6, Enright and Pryce #B1 7 3 Problem 7, Enright and Pryce #B2 8 3 Problem 8, Enright and Pryce #B3 9 3 Problem 9, Enright and Pryce #B4 10 3 Problem 10, Enright and Pryce #B5 11 10 Problem 11, Enright and Pryce #C1 12 10 Problem 12, Enright and Pryce #C2 13 10 Problem 13, Enright and Pryce #C3 14 51 Problem 14, Enright and Pryce #C4 15 30 Problem 15, Enright and Pryce #C5 16 4 Problem 16, Enright and Pryce #D1 17 4 Problem 17, Enright and Pryce #D2 18 4 Problem 18, Enright and Pryce #D3 19 4 Problem 19, Enright and Pryce #D4 20 4 Problem 20, Enright and Pryce #D5 21 2 Problem 21, Enright and Pryce #E1 22 2 Problem 22, Enright and Pryce #E2 23 2 Problem 23, Enright and Pryce #E3 24 2 Problem 24, Enright and Pryce #E4 25 2 Problem 25, Enright and Pryce #E5 26 2 Problem 26, Enright and Pryce #F1 27 1 Problem 27, Enright and Pryce #F2 28 2 Problem 28, Enright and Pryce #F3 29 1 Problem 29, Enright and Pryce #F4 30 1 Problem 30, Enright and Pryce #F5 31 2 Problem 31, Lotka-Volterra Predator-Prey Equations. 32 3 Problem 32, The Lorenz System 33 2 Problem 33, The Van der Pol equation 34 2 Problem 34, The Linearized Damped Pendulum 35 2 Problem 35, The Nonlinear Damped Pendulum 36 2 Problem 36, Duffing's Equation 37 2 Problem 37, Duffing's Equation with Damping and Forcing 38 1 Problem 38, Shampine's Ball of Flame 39 1 Problem 39, Polking's First Order System 40 1 Problem 40, The Knee Problem TEST02 Solve problems using an Euler method. The number of steps taken is 500 The number of tests available 40 EULER_TEST Problem number = 1 Problem 1, Enright and Pryce #A1, exponential decay. The system is autonomous. Number of equations is 1 Stepsize H = 0.040000 0.000000 1.000000 2.000000 0.129886 4.000000 0.016870 6.000000 0.002191 8.000000 0.000285 10.000000 0.000037 12.000000 0.000005 14.000000 0.000001 16.000000 0.000000 18.000000 0.000000 20.000000 0.000000 Expected final conditions: 20.000000 0.000000 EULER_TEST Problem number = 2 Problem 2, Enright and Pryce #A2 The system is autonomous. Number of equations is 1 Stepsize H = 0.040000 0.000000 1.000000 2.000000 0.574140 4.000000 0.445039 6.000000 0.376380 8.000000 0.332107 10.000000 0.300521 12.000000 0.276526 14.000000 0.257497 16.000000 0.241927 18.000000 0.228881 20.000000 0.217742 Expected final conditions: 20.000000 0.218218 EULER_TEST Problem number = 3 Problem 3, Enright and Pryce #A3 The system is not autonomous. Number of equations is 1 Stepsize H = 0.040000 0.000000 1.000000 2.000000 2.512564 4.000000 0.463410 6.000000 0.714545 8.000000 2.543402 10.000000 0.542180 12.000000 0.522416 14.000000 2.378037 16.000000 0.662504 18.000000 0.398605 20.000000 2.056168 Expected final conditions: 20.000000 2.491650 EULER_TEST Problem number = 4 Problem 4, Enright and Pryce #A4 The system is autonomous. Number of equations is 1 Stepsize H = 0.040000 0.000000 1.000000 2.000000 1.593739 4.000000 2.494134 6.000000 3.799076 8.000000 5.571079 10.000000 7.775402 12.000000 10.236266 14.000000 12.671700 16.000000 14.810011 18.000000 16.498273 20.000000 17.722575 Expected final conditions: 20.000000 17.730166 EULER_TEST Problem number = 5 Problem 5, Enright and Pryce #A5 The system is not autonomous. Number of equations is 1 Stepsize H = 0.040000 0.000000 4.000000 2.000000 5.368569 4.000000 6.012416 6.000000 6.228491 8.000000 6.113355 10.000000 5.708009 12.000000 5.028118 14.000000 4.073386 16.000000 2.830082 18.000000 1.269789 20.000000 -0.655739 Expected final conditions: 20.000000 -0.788783 EULER_TEST Problem number = 6 Problem 6, Enright and Pryce #B1 The system is autonomous. Number of equations is 2 Stepsize H = 0.040000 0.000000 1.000000 3.000000 2.000000 0.068873 0.549361 4.000000 1.180478 0.144933 6.000000 0.126499 2.941456 8.000000 0.031220 0.408280 10.000000 0.723914 0.079774 12.000000 0.350035 4.457348 14.000000 0.003556 0.617137 16.000000 0.060558 0.083069 18.000000 2.417556 0.037290 20.000000 0.000918 3.111140 Expected final conditions: 20.000000 0.676188 0.186082 EULER_TEST Problem number = 7 Problem 7, Enright and Pryce #B2 The system is autonomous. Number of equations is 3 Stepsize H = 0.040000 0.000000 2.000000 0.000000 1.000000 2.000000 1.065781 0.998325 0.935895 4.000000 1.008437 0.999997 0.991566 6.000000 1.001096 1.000000 0.998904 8.000000 1.000142 1.000000 0.999858 10.000000 1.000018 1.000000 0.999982 12.000000 1.000002 1.000000 0.999998 14.000000 1.000000 1.000000 1.000000 16.000000 1.000000 1.000000 1.000000 18.000000 1.000000 1.000000 1.000000 20.000000 1.000000 1.000000 1.000000 Expected final conditions: 20.000000 1.000000 1.000000 1.000000 EULER_TEST Problem number = 8 Problem 8, Enright and Pryce #B3 The system is autonomous. Number of equations is 3 Stepsize H = 0.040000 0.000000 1.000000 0.000000 0.000000 2.000000 0.129886 0.479223 0.390891 4.000000 0.016870 0.294023 0.689107 6.000000 0.002191 0.192988 0.804820 8.000000 0.000285 0.140272 0.859443 10.000000 0.000037 0.109604 0.890359 12.000000 0.000005 0.089859 0.910136 14.000000 0.000001 0.076135 0.923865 16.000000 0.000000 0.066049 0.933951 18.000000 0.000000 0.058325 0.941675 20.000000 0.000000 0.052220 0.947780 Expected final conditions: 20.000000 0.000000 0.052572 0.947428 EULER_TEST Problem number = 9 Problem 9, Enright and Pryce #B4 The system is autonomous. Number of equations is 3 Stepsize H = 0.040000 0.000000 3.000000 0.000000 0.000000 2.000000 -0.739391 1.519403 0.923267 4.000000 -0.913878 -1.125949 -0.743785 6.000000 3.018200 -0.876938 -0.275834 8.000000 -0.348920 2.134450 1.007112 10.000000 -1.207031 -0.838989 -0.528146 12.000000 2.713235 -1.718774 -0.528275 14.000000 0.335416 2.624421 1.009427 16.000000 -1.480617 -0.497059 -0.268500 18.000000 2.134704 -2.410067 -0.737210 20.000000 1.256858 2.853779 0.930950 Expected final conditions: 20.000000 0.982695 2.198447 0.912945 EULER_TEST Problem number = 10 Problem 10, Enright and Pryce #B5 The system is autonomous. Number of equations is 3 Stepsize H = 0.040000 0.000000 0.000000 1.000000 1.000000 2.000000 1.023702 -0.102548 0.695452 4.000000 -0.290064 -1.020915 1.000230 6.000000 -1.044338 0.307592 0.708338 8.000000 0.592492 0.958292 0.956122 10.000000 1.024336 -0.528044 0.754528 12.000000 -0.872562 -0.817636 0.872513 14.000000 -0.950343 0.766225 0.835960 16.000000 1.105368 0.622348 0.767971 18.000000 0.799459 -1.018374 0.948477 20.000000 -1.283904 -0.400900 0.666120 Expected final conditions: 20.000000 -0.939657 -0.342118 0.741413 EULER_TEST Problem number = 11 Problem 11, Enright and Pryce #C1 The system is autonomous. Number of equations is 10 The system is large. Print only MIN, AVERAGE, MAX and L2NORM. Stepsize H = 0.040000 0.000000 0.000000 0.100000 1.000000 1.000000 2.000000 0.000148 0.100000 0.276233 0.457994 4.000000 0.016870 0.100000 0.199388 0.382230 6.000000 0.002191 0.100000 0.163932 0.365608 8.000000 0.000285 0.100000 0.407433 0.483293 10.000000 0.000037 0.100000 0.671789 0.691172 12.000000 0.000005 0.100000 0.850291 0.854231 14.000000 0.000001 0.100000 0.941604 0.942239 16.000000 0.000000 0.100000 0.979907 0.979988 18.000000 0.000000 0.100000 0.993753 0.993762 20.000000 0.000000 0.100000 0.998213 0.998214 Expected final conditions: 20.000000 0.000000 0.100000 0.997913 0.997914 EULER_TEST Problem number = 12 Problem 12, Enright and Pryce #C2 The system is autonomous. Number of equations is 10 The system is large. Print only MIN, AVERAGE, MAX and L2NORM. Stepsize H = 0.040000 0.000000 0.000000 0.100000 1.000000 1.000000 2.000000 0.044841 0.100000 0.265996 0.370675 4.000000 0.015034 0.100000 0.856546 0.857882 6.000000 0.002162 0.100000 0.980412 0.980434 8.000000 0.000284 0.100000 0.997441 0.997441 10.000000 0.000037 0.100000 0.999667 0.999667 12.000000 0.000005 0.100000 0.999957 0.999957 14.000000 0.000001 0.100000 0.999994 0.999994 16.000000 0.000000 0.100000 0.999999 0.999999 18.000000 0.000000 0.100000 1.000000 1.000000 20.000000 0.000000 0.100000 1.000000 1.000000 Expected final conditions: 20.000000 0.000000 0.100000 1.000000 1.000000 EULER_TEST Problem number = 13 Problem 13, Enright and Pryce #C3 The system is autonomous. Number of equations is 10 The system is large. Print only MIN, AVERAGE, MAX and L2NORM. Stepsize H = 0.040000 0.000000 0.000000 0.100000 1.000000 1.000000 2.000000 0.000028 0.038331 0.116251 0.181551 4.000000 0.000826 0.027599 0.059071 0.109812 6.000000 0.002503 0.022346 0.039171 0.081379 8.000000 0.003790 0.018726 0.029955 0.065277 10.000000 0.004328 0.015853 0.023704 0.054193 12.000000 0.004325 0.013462 0.019719 0.045642 14.000000 0.004033 0.011441 0.016589 0.038662 16.000000 0.003621 0.009726 0.014006 0.032824 18.000000 0.003181 0.008269 0.011855 0.027891 20.000000 0.002759 0.007030 0.010051 0.023708 Expected final conditions: 20.000000 0.002762 0.007049 0.010079 0.023771 EULER_TEST Problem number = 14 Problem 14, Enright and Pryce #C4 The system is autonomous. Number of equations is 51 The system is large. Print only MIN, AVERAGE, MAX and L2NORM. Stepsize H = 0.040000 0.000000 0.000000 0.019608 1.000000 1.000000 2.000000 0.000000 0.007516 0.116251 0.181551 4.000000 0.000000 0.005424 0.059071 0.109815 6.000000 0.000000 0.004458 0.039171 0.081474 8.000000 0.000000 0.003873 0.029970 0.065845 10.000000 0.000000 0.003471 0.023767 0.055791 12.000000 0.000000 0.003173 0.020031 0.048714 14.000000 0.000000 0.002940 0.017147 0.043430 16.000000 0.000000 0.002752 0.014996 0.039314 18.000000 0.000000 0.002596 0.013389 0.036007 20.000000 0.000000 0.002464 0.012025 0.033283 Expected final conditions: 20.000000 0.000000 0.002466 0.012045 0.033314 EULER_TEST Problem number = 15 Problem 15, Enright and Pryce #C5 This problem has 7 parameters. The system is autonomous. Number of equations is 30 The system is large. Print only MIN, AVERAGE, MAX and L2NORM. Stepsize H = 0.040000 0.000000 -30.155227 1.674518 28.446510 53.844833 2.000000 -30.197135 1.600758 28.010686 53.735231 4.000000 -30.226324 1.493850 27.568643 53.627579 6.000000 -30.242655 1.358088 27.120383 53.521531 8.000000 -30.245996 1.199287 26.665948 53.416677 10.000000 -30.236236 1.024038 26.205413 53.312583 12.000000 -30.213293 0.839106 25.738879 53.208838 14.000000 -30.177116 0.650979 25.266464 53.105078 16.000000 -30.127685 0.465574 24.788296 53.001018 18.000000 -30.065009 0.288037 24.304507 52.896466 20.000000 -29.989126 0.122618 23.815230 52.791330 Expected final conditions: 20.000000 -29.987593 0.126877 23.814590 52.766797 EULER_TEST Problem number = 16 Problem 16, Enright and Pryce #D1 This problem has 1 parameters. The system is autonomous. Number of equations is 4 Stepsize H = 0.040000 0.000000 0.900000 0.000000 0.000000 1.105542 2.000000 -0.586227 1.009612 -0.887472 -0.314702 4.000000 -1.427480 -0.307350 0.086429 -0.765272 6.000000 -0.517198 -1.404892 0.736555 -0.214687 8.000000 0.954248 -0.938356 0.545718 0.697838 10.000000 0.999287 0.805188 -0.559590 0.773256 12.000000 -0.590537 1.431946 -0.814484 -0.159596 14.000000 -1.778984 0.564467 -0.327949 -0.616122 16.000000 -1.920980 -0.715580 0.178915 -0.607343 18.000000 -1.176165 -1.693022 0.543898 -0.327864 20.000000 0.095835 -1.913918 0.682299 0.143165 Expected final conditions: 20.000000 0.219884 0.942708 -0.978766 0.328798 EULER_TEST Problem number = 17 Problem 17, Enright and Pryce #D2 This problem has 1 parameters. The system is autonomous. Number of equations is 4 Stepsize H = 0.040000 0.000000 0.700000 0.000000 0.000000 1.362770 2.000000 -0.961448 0.988229 -0.795780 -0.287437 4.000000 -1.871247 0.008950 -0.130991 -0.577877 6.000000 -1.616657 -1.052398 0.375901 -0.432356 8.000000 -0.464973 -1.513728 0.750832 0.056708 10.000000 0.920125 -0.416680 0.296045 1.123372 12.000000 -0.094522 1.392017 -0.910507 0.339105 14.000000 -1.670603 1.385767 -0.625287 -0.232313 16.000000 -2.622338 0.736282 -0.332055 -0.387838 18.000000 -3.048137 -0.081774 -0.096464 -0.417824 20.000000 -3.039121 -0.895068 0.105537 -0.386481 Expected final conditions: 20.000000 -0.177703 0.946778 -1.030294 0.121107 EULER_TEST Problem number = 18 Problem 18, Enright and Pryce #D3 This problem has 1 parameters. The system is autonomous. Number of equations is 4 Stepsize H = 0.040000 0.000000 0.500000 0.000000 0.000000 1.732051 2.000000 -1.382099 1.047906 -0.793315 -0.129720 4.000000 -2.549678 0.558469 -0.406474 -0.310582 6.000000 -3.113318 -0.096469 -0.165686 -0.333513 8.000000 -3.255045 -0.745671 0.022531 -0.309657 10.000000 -3.042612 -1.316207 0.191974 -0.254471 12.000000 -2.493216 -1.740781 0.362512 -0.159791 14.000000 -1.586525 -1.909822 0.552993 0.014377 16.000000 -0.270893 -1.533278 0.761443 0.456658 18.000000 0.542711 0.592226 -0.768091 1.306495 20.000000 -1.337728 1.769894 -0.848222 0.214875 Expected final conditions: 20.000000 -0.578043 0.863384 -0.959508 -0.065049 EULER_TEST Problem number = 19 Problem 19, Enright and Pryce #D4 This problem has 1 parameters. The system is autonomous. Number of equations is 4 Stepsize H = 0.040000 0.000000 0.300000 0.000000 0.000000 2.380476 2.000000 -2.121406 1.501274 -1.063722 0.308275 4.000000 -4.082057 2.013013 -0.918754 0.221597 6.000000 -5.850801 2.424161 -0.855387 0.192829 8.000000 -7.522761 2.794296 -0.818649 0.178385 10.000000 -9.134716 3.141883 -0.794290 0.169666 12.000000 -10.705282 3.475135 -0.776801 0.163817 14.000000 -12.245343 3.798437 -0.763561 0.159613 16.000000 -13.761874 4.114417 -0.753151 0.156441 18.000000 -15.259643 4.424773 -0.744729 0.153960 20.000000 -16.742065 4.730670 -0.737762 0.151965 Expected final conditions: 20.000000 -0.953899 0.690741 -0.821267 -0.153957 EULER_TEST Problem number = 20 Problem 20, Enright and Pryce #D5 This problem has 1 parameters. The system is autonomous. Number of equations is 4 Stepsize H = 0.040000 0.000000 0.100000 0.000000 0.000000 4.358899 2.000000 -8.180687 5.921357 -4.188342 2.856474 4.000000 -16.547600 11.627307 -4.180251 2.850702 6.000000 -24.905101 17.326609 -4.177558 2.848819 8.000000 -33.258769 23.023240 -4.176211 2.847884 10.000000 -41.610340 28.718419 -4.175403 2.847325 12.000000 -49.960585 34.412683 -4.174864 2.846954 14.000000 -58.309917 40.106317 -4.174480 2.846689 16.000000 -66.658581 45.799492 -4.174191 2.846490 18.000000 -75.006733 51.492316 -4.173966 2.846336 20.000000 -83.354483 57.184863 -4.173787 2.846213 Expected final conditions: 20.000000 -1.295266 0.400394 -0.677539 -0.127084 EULER_TEST Problem number = 21 Problem 21, Enright and Pryce #E1 The system is autonomous. Number of equations is 2 Stepsize H = 0.040000 0.000000 0.671397 0.095401 2.000000 0.061891 -0.480441 4.000000 -0.363253 0.151809 6.000000 0.226359 0.230530 8.000000 0.118283 -0.290063 10.000000 -0.288875 0.023809 12.000000 0.124902 0.242082 14.000000 0.166758 -0.215429 16.000000 -0.254471 -0.054995 18.000000 0.048606 0.252045 20.000000 0.207866 -0.153260 Expected final conditions: 20.000000 0.145672 -0.098835 EULER_TEST Problem number = 22 Problem 22, Enright and Pryce #E2 The system is autonomous. Number of equations is 2 Stepsize H = 0.040000 0.000000 2.000000 0.000000 2.000000 0.365057 -1.782742 4.000000 -1.823540 0.615083 6.000000 0.933563 2.731913 8.000000 1.418775 -0.856738 10.000000 -2.023719 -0.593265 12.000000 -0.835665 1.311487 14.000000 1.992333 -0.463725 16.000000 -0.131546 -2.304361 18.000000 -1.661380 0.712237 20.000000 1.569341 2.131156 Expected final conditions: 20.000000 2.008150 -0.042509 EULER_TEST Problem number = 23 Problem 23, Enright and Pryce #E3 The system is autonomous. Number of equations is 2 Stepsize H = 0.040000 0.000000 0.000000 0.000000 2.000000 1.076211 -0.741100 4.000000 -0.162926 -0.815062 6.000000 -0.484191 1.070742 8.000000 0.903669 1.246878 10.000000 0.201687 -0.208941 12.000000 -1.376610 0.161353 14.000000 -0.148877 0.826544 16.000000 1.128099 -0.911859 18.000000 -0.545263 -1.915166 20.000000 -1.126847 0.123699 Expected final conditions: 20.000000 -0.100418 0.241140 EULER_TEST Problem number = 24 Problem 24, Enright and Pryce #E4 The system is autonomous. Number of equations is 2 Stepsize H = 0.040000 0.000000 30.000000 0.000000 2.000000 30.062223 0.062960 4.000000 30.245462 0.120027 6.000000 30.533628 0.167269 8.000000 30.905494 0.203524 10.000000 31.339771 0.229759 12.000000 31.818271 0.247944 14.000000 32.326978 0.260177 16.000000 32.855805 0.268242 18.000000 33.397807 0.273486 20.000000 33.948342 0.276868 Expected final conditions: 20.000000 33.950914 0.276782 EULER_TEST Problem number = 25 Problem 25, Enright and Pryce #E5 The system is not autonomous. Number of equations is 2 Stepsize H = 0.040000 0.000000 0.000000 0.000000 2.000000 0.080533 0.083406 4.000000 0.335611 0.175070 6.000000 0.784145 0.277596 8.000000 1.451349 0.394809 10.000000 2.371906 0.532570 12.000000 3.595383 0.700335 14.000000 5.196197 0.914412 16.000000 7.293622 1.205543 18.000000 10.097137 1.639402 20.000000 14.029129 2.385911 Expected final conditions: 20.000000 14.117974 2.400000 EULER_TEST Problem number = 26 Problem 26, Enright and Pryce #F1 This problem has 1 parameters. The system is autonomous. Number of equations is 2 Stepsize H = 0.040000 0.000000 0.000000 0.000000 2.000000 -0.555314 -0.057407 4.000000 -1.553592 -0.340860 6.000000 -3.342253 -1.173883 8.000000 -6.536386 -3.249930 10.000000 -12.221008 -8.013263 12.000000 -22.302832 -18.408170 14.000000 -40.119171 -40.337736 16.000000 -71.486663 -85.479456 18.000000 -126.497510 -176.678645 20.000000 -222.577263 -358.210573 Expected final conditions: 20.000000 -12.944606 -0.000000 EULER_TEST Problem number = 27 Problem 27, Enright and Pryce #F2 The system is not autonomous. Number of equations is 1 Stepsize H = 0.040000 0.000000 110.000000 2.000000 75.168062 4.000000 70.692724 6.000000 70.117716 8.000000 70.043836 10.000000 70.034344 12.000000 70.033124 14.000000 70.032968 16.000000 70.032948 18.000000 70.032945 20.000000 70.032945 Expected final conditions: 20.000000 70.037311 EULER_TEST Problem number = 29 Problem 29, Enright and Pryce #F4 The system is not autonomous. Number of equations is 1 Stepsize H = 0.040000 0.000000 1.000000 2.000000 15.797034 4.000000 45.344863 6.000000 46.114387 8.000000 15.614795 10.000000 0.285243 12.000000 0.000736 14.000000 0.000011 16.000000 0.000000 18.000000 0.000000 20.000000 0.000000 Expected final conditions: 20.000000 0.000000 EULER_TEST Problem number = 30 Problem 30, Enright and Pryce #F5 The system is not autonomous. Number of equations is 1 Stepsize H = 0.040000 0.000000 1.000000 2.000000 0.801068 4.000000 0.671236 6.000000 0.590582 8.000000 0.546518 10.000000 0.532350 12.000000 0.545947 14.000000 0.589292 16.000000 0.668885 18.000000 0.797008 20.000000 0.993199 Expected final conditions: 20.000000 1.000000 EULER_TEST Problem number = 31 Problem 31, Lotka-Volterra Predator-Prey Equations. This problem has 4 parameters. The system is autonomous. Number of equations is 2 Stepsize H = 0.040000 0.000000 2.000000 2.000000 2.000000 0.298384 2.443350 4.000000 0.007349 8.692192 6.000000 1.361171 0.157248 8.000000 -0.000000 5.328440 10.000000 -0.000003 0.082412 12.000000 -0.025450 0.001271 14.000000 -231.496580 0.000000 16.000000 Inf -Inf 18.000000 Inf -Inf 20.000000 Inf -Inf Expected final conditions: 20.000000 2.200500 10.272600 EULER_TEST Problem number = 32 Problem 32, The Lorenz System This problem has 3 parameters. The system is autonomous. Number of equations is 3 Stepsize H = 0.040000 0.000000 2.000000 2.000000 21.000000 2.000000 NaN NaN NaN 4.000000 NaN NaN NaN 6.000000 NaN NaN NaN 8.000000 NaN NaN NaN 10.000000 NaN NaN NaN 12.000000 NaN NaN NaN 14.000000 NaN NaN NaN 16.000000 NaN NaN NaN 18.000000 NaN NaN NaN 20.000000 NaN NaN NaN Expected final conditions: 20.000000 0.000000 0.000000 0.000000 EULER_TEST Problem number = 33 Problem 33, The Van der Pol equation This problem has 1 parameters. The system is autonomous. Number of equations is 2 Stepsize H = 0.040000 0.000000 2.000000 2.000000 2.000000 1.437125 -0.857275 4.000000 -2.015265 -0.653273 6.000000 -0.857082 1.291832 8.000000 1.999792 -0.452663 10.000000 -0.093978 -2.268089 12.000000 -1.673120 0.705521 14.000000 1.531597 2.204137 16.000000 1.208077 -1.001008 18.000000 -2.086753 0.083982 20.000000 -0.503607 1.641255 Expected final conditions: 20.000000 0.756245 2.672940 EULER_TEST Problem number = 34 Problem 34, The Linearized Damped Pendulum This problem has 4 parameters. The system is autonomous. Number of equations is 2 Stepsize H = 0.040000 0.000000 2.000000 2.000000 2.000000 0.128779 15.324728 4.000000 -3.387545 8.756879 6.000000 -2.932034 -19.746805 8.000000 3.568803 -31.064194 10.000000 7.969223 9.636611 12.000000 0.140522 61.915675 14.000000 -13.795836 32.664157 16.000000 -11.270712 -81.952380 18.000000 15.069508 -122.501889 20.000000 31.713375 45.123816 Expected final conditions: 20.000000 0.000070 0.000278 EULER_TEST Problem number = 35 Problem 35, The Nonlinear Damped Pendulum This problem has 4 parameters. The system is autonomous. Number of equations is 2 Stepsize H = 0.040000 0.000000 2.000000 2.000000 2.000000 -0.936744 -6.350458 4.000000 0.982658 5.353765 6.000000 -1.258832 -3.062968 8.000000 1.424793 0.142207 10.000000 -1.332536 2.858703 12.000000 0.940379 -5.551911 14.000000 -0.283944 7.158405 16.000000 -0.483769 -6.517969 18.000000 1.104313 3.694738 20.000000 -1.384112 -0.154747 Expected final conditions: 20.000000 -0.000058 0.000360 EULER_TEST Problem number = 38 Problem 38, Shampine's Ball of Flame This problem has 1 parameters. The system is autonomous. Number of equations is 1 Stepsize H = 0.400000 0.000000 0.010000 20.000000 0.012452 40.000000 0.016473 60.000000 0.024242 80.000000 0.045172 100.000000 0.221404 120.000000 1.000000 140.000000 1.000000 160.000000 1.000000 180.000000 1.000000 200.000000 1.000000 Expected final conditions: 200.000000 1.000000 EULER_TEST Problem number = 39 Problem 39, Polking's First Order System This problem has 2 parameters. The system is not autonomous. Number of equations is 1 Stepsize H = 0.018000 0.000000 0.500000 0.900000 0.323498 1.800000 -0.762258 2.700000 -1.490970 3.600000 -1.817672 4.500000 -2.061378 5.400000 -2.274895 6.300000 -2.468589 7.200000 -2.647363 8.100000 -2.814308 9.000000 -2.971556 Expected final conditions: 9.000000 -3.000000 EULER_TEST Problem number = 40 Problem 40, The Knee Problem This problem has 1 parameters. The system is not autonomous. Number of equations is 1 Stepsize H = 0.004000 -1.000000 -1.000000 -0.800000 -0.812136 -0.600000 -0.615846 -0.400000 -0.422554 -0.200000 -0.237288 0.000000 -0.079602 0.200000 -0.005258 0.400000 -0.000009 0.600000 -0.000000 0.800000 -0.000000 1.000000 -0.000000 Expected final conditions: 1.000000 -0.000000 TEST03 Solve problems using a Runge-Kutta method. The number of steps taken is 500 The number of tests available 40 RK_TEST Problem number = 1 Runge-Kutta order = 3 Problem 1, Enright and Pryce #A1, exponential decay. The system is autonomous. Number of equations is 1 Stepsize H = 0.040000 0.000000 1.000000 2.000000 0.135335 4.000000 0.018315 6.000000 0.002479 8.000000 0.000335 10.000000 0.000045 12.000000 0.000006 14.000000 0.000001 16.000000 0.000000 18.000000 0.000000 20.000000 0.000000 Expected final conditions: 20.000000 0.000000 RK_TEST Problem number = 2 Runge-Kutta order = 3 Problem 2, Enright and Pryce #A2 The system is autonomous. Number of equations is 1 Stepsize H = 0.040000 0.000000 1.000000 2.000000 0.577350 4.000000 0.447214 6.000000 0.377964 8.000000 0.333333 10.000000 0.301511 12.000000 0.277350 14.000000 0.258199 16.000000 0.242536 18.000000 0.229416 20.000000 0.218218 Expected final conditions: 20.000000 0.218218 RK_TEST Problem number = 3 Runge-Kutta order = 3 Problem 3, Enright and Pryce #A3 The system is not autonomous. Number of equations is 1 Stepsize H = 0.040000 0.000000 1.000000 2.000000 2.482582 4.000000 0.469164 6.000000 0.756228 8.000000 2.689516 10.000000 0.580411 12.000000 0.584752 14.000000 2.692881 16.000000 0.749837 18.000000 0.471904 20.000000 2.491665 Expected final conditions: 20.000000 2.491650 RK_TEST Problem number = 4 Runge-Kutta order = 3 Problem 4, Enright and Pryce #A4 The system is autonomous. Number of equations is 1 Stepsize H = 0.040000 0.000000 1.000000 2.000000 1.596923 4.000000 2.503220 6.000000 3.817178 8.000000 5.600091 10.000000 7.813675 12.000000 10.277733 14.000000 12.708496 16.000000 14.836827 18.000000 16.514309 20.000000 17.730166 Expected final conditions: 20.000000 17.730166 RK_TEST Problem number = 5 Runge-Kutta order = 3 Problem 5, Enright and Pryce #A5 The system is not autonomous. Number of equations is 1 Stepsize H = 0.040000 0.000000 4.000000 2.000000 5.356837 4.000000 5.993114 6.000000 6.201854 8.000000 6.078755 10.000000 5.664306 12.000000 4.973658 14.000000 4.005864 16.000000 2.746253 18.000000 1.164945 20.000000 -0.788783 Expected final conditions: 20.000000 -0.788783 RK_TEST Problem number = 6 Runge-Kutta order = 3 Problem 6, Enright and Pryce #B1 The system is autonomous. Number of equations is 2 Stepsize H = 0.040000 0.000000 1.000000 3.000000 2.000000 0.084961 0.577949 4.000000 1.446357 0.187187 6.000000 0.175577 2.258932 8.000000 0.147120 0.366734 10.000000 3.142907 0.348408 12.000000 0.075672 1.433380 14.000000 0.300981 0.245158 16.000000 3.963416 1.541600 18.000000 0.065519 0.889725 20.000000 0.674238 0.186039 Expected final conditions: 20.000000 0.676188 0.186082 RK_TEST Problem number = 7 Runge-Kutta order = 3 Problem 7, Enright and Pryce #B2 The system is autonomous. Number of equations is 3 Stepsize H = 0.040000 0.000000 2.000000 0.000000 1.000000 2.000000 1.068906 0.997522 0.933572 4.000000 1.009161 0.999994 0.990845 6.000000 1.001239 1.000000 0.998761 8.000000 1.000168 1.000000 0.999832 10.000000 1.000023 1.000000 0.999977 12.000000 1.000003 1.000000 0.999997 14.000000 1.000000 1.000000 1.000000 16.000000 1.000000 1.000000 1.000000 18.000000 1.000000 1.000000 1.000000 20.000000 1.000000 1.000000 1.000000 Expected final conditions: 20.000000 1.000000 1.000000 1.000000 RK_TEST Problem number = 8 Runge-Kutta order = 3 Problem 8, Enright and Pryce #B3 The system is autonomous. Number of equations is 3 Stepsize H = 0.040000 0.000000 1.000000 0.000000 0.000000 2.000000 0.135335 0.478424 0.386242 4.000000 0.018315 0.297188 0.684496 6.000000 0.002479 0.195491 0.802030 8.000000 0.000335 0.141977 0.857688 10.000000 0.000045 0.110791 0.889164 12.000000 0.000006 0.090725 0.909269 14.000000 0.000001 0.076796 0.923204 16.000000 0.000000 0.066571 0.933428 18.000000 0.000000 0.058749 0.941251 20.000000 0.000000 0.052572 0.947428 Expected final conditions: 20.000000 0.000000 0.052572 0.947428 RK_TEST Problem number = 9 Runge-Kutta order = 3 Problem 9, Enright and Pryce #B4 The system is autonomous. Number of equations is 3 Stepsize H = 0.040000 0.000000 3.000000 0.000000 0.000000 2.000000 -0.659103 1.440188 0.909296 4.000000 -0.880038 -1.018912 -0.756803 6.000000 2.842255 -0.827116 -0.279418 8.000000 -0.269818 1.834745 0.989354 10.000000 -0.974092 -0.631551 -0.544022 12.000000 2.399781 -1.525931 -0.536578 14.000000 0.292178 2.116645 0.990601 16.000000 -0.998195 -0.300078 -0.287905 18.000000 1.756639 -1.997863 -0.750995 20.000000 0.982699 2.198432 0.912937 Expected final conditions: 20.000000 0.982695 2.198447 0.912945 RK_TEST Problem number = 10 Runge-Kutta order = 3 Problem 10, Enright and Pryce #B5 The system is autonomous. Number of equations is 3 Stepsize H = 0.040000 0.000000 0.000000 1.000000 1.000000 2.000000 0.995363 -0.096156 0.703360 4.000000 -0.269604 -0.962965 0.981287 6.000000 -0.957499 0.288404 0.729672 8.000000 0.510895 0.859628 0.931060 10.000000 0.877890 -0.478832 0.779060 12.000000 -0.705371 -0.708811 0.863848 14.000000 -0.750432 0.660916 0.844260 16.000000 0.847241 0.531161 0.796173 18.000000 0.570605 -0.821191 0.913195 20.000000 -0.939613 -0.342146 0.741423 Expected final conditions: 20.000000 -0.939657 -0.342118 0.741413 RK_TEST Problem number = 11 Runge-Kutta order = 3 Problem 11, Enright and Pryce #C1 The system is autonomous. Number of equations is 10 The system is large. Print only MIN, AVERAGE, MAX and L2NORM. Stepsize H = 0.040000 0.000000 0.000000 0.100000 1.000000 1.000000 2.000000 0.000237 0.100000 0.270672 0.454975 4.000000 0.018315 0.100000 0.195367 0.379053 6.000000 0.002479 0.100000 0.160623 0.364212 8.000000 0.000335 0.100000 0.407453 0.482198 10.000000 0.000045 0.100000 0.667180 0.686841 12.000000 0.000006 0.100000 0.844972 0.849130 14.000000 0.000001 0.100000 0.937945 0.938648 16.000000 0.000000 0.100000 0.978013 0.978109 18.000000 0.000000 0.100000 0.992944 0.992955 20.000000 0.000000 0.100000 0.997913 0.997914 Expected final conditions: 20.000000 0.000000 0.100000 0.997913 0.997914 RK_TEST Problem number = 12 Runge-Kutta order = 3 Problem 12, Enright and Pryce #C2 The system is autonomous. Number of equations is 10 The system is large. Print only MIN, AVERAGE, MAX and L2NORM. Stepsize H = 0.040000 0.000000 0.000000 0.100000 1.000000 1.000000 2.000000 0.042284 0.100000 0.270164 0.374527 4.000000 0.015798 0.100000 0.846734 0.848277 6.000000 0.002430 0.100000 0.977911 0.977939 8.000000 0.000335 0.100000 0.996985 0.996985 10.000000 0.000045 0.100000 0.999591 0.999591 12.000000 0.000006 0.100000 0.999945 0.999945 14.000000 0.000001 0.100000 0.999993 0.999993 16.000000 0.000000 0.100000 0.999999 0.999999 18.000000 0.000000 0.100000 1.000000 1.000000 20.000000 0.000000 0.100000 1.000000 1.000000 Expected final conditions: 20.000000 0.000000 0.100000 1.000000 1.000000 RK_TEST Problem number = 13 Runge-Kutta order = 3 Problem 13, Enright and Pryce #C3 The system is autonomous. Number of equations is 10 The system is large. Print only MIN, AVERAGE, MAX and L2NORM. Stepsize H = 0.040000 0.000000 0.000000 0.100000 1.000000 1.000000 2.000000 0.000036 0.038574 0.117627 0.183127 4.000000 0.000846 0.027690 0.059396 0.110308 6.000000 0.002488 0.022391 0.039423 0.081623 8.000000 0.003759 0.018754 0.030061 0.065423 10.000000 0.004301 0.015877 0.023790 0.054297 12.000000 0.004308 0.013484 0.019761 0.045727 14.000000 0.004025 0.011462 0.016627 0.038738 16.000000 0.003619 0.009747 0.014041 0.032895 18.000000 0.003183 0.008289 0.011886 0.027958 20.000000 0.002762 0.007049 0.010079 0.023771 Expected final conditions: 20.000000 0.002762 0.007049 0.010079 0.023771 RK_TEST Problem number = 14 Runge-Kutta order = 3 Problem 14, Enright and Pryce #C4 The system is autonomous. Number of equations is 51 The system is large. Print only MIN, AVERAGE, MAX and L2NORM. Stepsize H = 0.040000 0.000000 0.000000 0.019608 1.000000 1.000000 2.000000 0.000000 0.007564 0.117627 0.183127 4.000000 0.000000 0.005443 0.059396 0.110312 6.000000 0.000000 0.004468 0.039424 0.081723 8.000000 0.000000 0.003880 0.030077 0.065997 10.000000 0.000000 0.003476 0.023856 0.055894 12.000000 0.000000 0.003177 0.020077 0.048789 14.000000 0.000000 0.002943 0.017188 0.043487 16.000000 0.000000 0.002755 0.015018 0.039360 18.000000 0.000000 0.002598 0.013411 0.036044 20.000000 0.000000 0.002466 0.012045 0.033314 Expected final conditions: 20.000000 0.000000 0.002466 0.012045 0.033314 RK_TEST Problem number = 15 Runge-Kutta order = 3 Problem 15, Enright and Pryce #C5 This problem has 7 parameters. The system is autonomous. Number of equations is 30 The system is large. Print only MIN, AVERAGE, MAX and L2NORM. Stepsize H = 0.040000 0.000000 -30.155227 1.674518 28.446510 53.844833 2.000000 -30.197008 1.600392 28.010623 53.734271 4.000000 -30.226068 1.493095 27.568517 53.625525 6.000000 -30.242266 1.356925 27.120193 53.518132 8.000000 -30.245470 1.197712 26.665691 53.411583 10.000000 -30.235569 1.022108 26.205087 53.305372 12.000000 -30.212479 0.837004 25.738483 53.199045 14.000000 -30.176144 0.649100 25.265998 53.092227 16.000000 -30.126541 0.464601 24.787762 52.984653 18.000000 -30.063679 0.288995 24.303913 52.876179 20.000000 -29.987593 0.126877 23.814590 52.766797 Expected final conditions: 20.000000 -29.987593 0.126877 23.814590 52.766797 RK_TEST Problem number = 16 Runge-Kutta order = 3 Problem 16, Enright and Pryce #D1 This problem has 1 parameters. The system is autonomous. Number of equations is 4 Stepsize H = 0.040000 0.000000 0.900000 0.000000 0.000000 1.105542 2.000000 -0.593536 0.865347 -0.828796 -0.468003 4.000000 -0.805444 -0.705108 0.662051 -0.655724 6.000000 0.851156 -0.307012 0.341025 1.045937 8.000000 -0.341132 0.965534 -0.947651 -0.234365 10.000000 -0.964691 -0.499433 0.462129 -0.792097 12.000000 0.711845 -0.580772 0.635397 0.879264 14.000000 -0.064446 0.994210 -1.002993 0.035417 16.000000 -1.064043 -0.263340 0.241510 -0.875244 18.000000 0.500642 -0.795298 0.850643 0.635929 20.000000 0.216372 0.943681 -0.979714 0.325050 Expected final conditions: 20.000000 0.219884 0.942708 -0.978766 0.328798 RK_TEST Problem number = 17 Runge-Kutta order = 3 Problem 17, Enright and Pryce #D2 This problem has 1 parameters. The system is autonomous. Number of equations is 4 Stepsize H = 0.040000 0.000000 0.700000 0.000000 0.000000 1.362770 2.000000 -0.917180 0.750470 -0.663793 -0.496907 4.000000 -1.082297 -0.593865 0.504361 -0.604625 6.000000 0.621567 -0.370244 0.536506 1.215075 8.000000 -0.708560 0.870357 -0.812958 -0.347583 10.000000 -1.200712 -0.413049 0.341108 -0.677057 12.000000 0.416811 -0.664979 0.888362 0.871117 14.000000 -0.462351 0.940858 -0.940902 -0.148222 16.000000 -1.272566 -0.217616 0.176804 -0.719261 18.000000 0.145419 -0.853765 1.033639 0.490249 20.000000 -0.187388 0.947432 -1.028522 0.110626 Expected final conditions: 20.000000 -0.177703 0.946778 -1.030294 0.121107 RK_TEST Problem number = 18 Runge-Kutta order = 3 Problem 18, Enright and Pryce #D3 This problem has 1 parameters. The system is autonomous. Number of equations is 4 Stepsize H = 0.040000 0.000000 0.500000 0.000000 0.000000 1.732051 2.000000 -1.205329 0.613050 -0.523259 -0.452281 4.000000 -1.332230 -0.478108 0.390362 -0.509893 6.000000 0.362725 -0.437726 0.889397 1.313909 8.000000 -1.041099 0.726054 -0.660414 -0.370996 10.000000 -1.418157 -0.334813 0.265730 -0.547732 12.000000 0.082512 -0.703309 1.147518 0.711051 14.000000 -0.847935 0.809140 -0.797236 -0.260013 16.000000 -1.469069 -0.190072 0.148611 -0.569954 18.000000 -0.207504 -0.826691 1.120937 0.294569 20.000000 -0.629457 0.855939 -0.930547 -0.109409 Expected final conditions: 20.000000 -0.578043 0.863384 -0.959508 -0.065049 RK_TEST Problem number = 19 Runge-Kutta order = 3 Problem 19, Enright and Pryce #D4 This problem has 1 parameters. The system is autonomous. Number of equations is 4 Stepsize H = 0.040000 0.000000 0.300000 0.000000 0.000000 2.380476 2.000000 -1.461309 0.448709 -0.407981 -0.362966 4.000000 -1.533363 -0.367842 0.330392 -0.386039 6.000000 0.145851 -0.379406 1.311397 1.479895 8.000000 -1.366103 0.492001 -0.470864 -0.351702 10.000000 -1.514048 -0.337514 0.310492 -0.401131 12.000000 0.154367 -0.368227 1.299665 1.512453 14.000000 -1.358073 0.466579 -0.450672 -0.368541 16.000000 -1.433248 -0.382817 0.369512 -0.397226 18.000000 0.299584 0.024512 -0.110228 2.361089 20.000000 -1.421134 0.366942 -0.344461 -0.410257 Expected final conditions: 20.000000 -0.953899 0.690741 -0.821267 -0.153957 RK_TEST Problem number = 20 Runge-Kutta order = 3 Problem 20, Enright and Pryce #D5 This problem has 1 parameters. The system is autonomous. Number of equations is 4 Stepsize H = 0.040000 0.000000 0.100000 0.000000 0.000000 4.358899 2.000000 -2.348330 1.973687 -1.016723 0.672361 4.000000 -4.270752 3.228595 -0.922390 0.597144 6.000000 -6.071182 4.389875 -0.882398 0.567575 8.000000 -7.811465 5.507453 -0.859692 0.551362 10.000000 -9.515116 6.599148 -0.844891 0.541012 12.000000 -11.193877 7.673559 -0.834417 0.533790 14.000000 -12.854532 8.735548 -0.826587 0.528446 16.000000 -14.501379 9.788151 -0.820498 0.524322 18.000000 -16.137328 10.833394 -0.815620 0.521038 20.000000 -17.764441 11.872704 -0.811619 0.518358 Expected final conditions: 20.000000 -1.295266 0.400394 -0.677539 -0.127084 RK_TEST Problem number = 21 Runge-Kutta order = 3 Problem 21, Enright and Pryce #E1 The system is autonomous. Number of equations is 2 Stepsize H = 0.040000 0.000000 0.671397 0.095401 2.000000 0.065010 -0.466882 4.000000 -0.342166 0.135431 6.000000 0.198125 0.213203 8.000000 0.109608 -0.248410 10.000000 -0.240564 0.011997 12.000000 0.092975 0.197231 14.000000 0.133965 -0.160964 16.000000 -0.186038 -0.047777 18.000000 0.027431 0.180250 20.000000 0.145666 -0.098828 Expected final conditions: 20.000000 0.145672 -0.098835 RK_TEST Problem number = 22 Runge-Kutta order = 3 Problem 22, Enright and Pryce #E2 The system is autonomous. Number of equations is 2 Stepsize H = 0.040000 0.000000 2.000000 0.000000 2.000000 0.323315 -1.832979 4.000000 -1.741744 0.624686 6.000000 1.279126 2.437678 8.000000 1.213156 -0.987873 10.000000 -2.008316 0.033065 12.000000 -0.313559 1.844252 14.000000 1.738546 -0.627227 16.000000 -1.291747 -2.422795 18.000000 -1.208026 0.991760 20.000000 2.008119 -0.042878 Expected final conditions: 20.000000 2.008150 -0.042509 RK_TEST Problem number = 23 Runge-Kutta order = 3 Problem 23, Enright and Pryce #E3 The system is autonomous. Number of equations is 2 Stepsize H = 0.040000 0.000000 0.000000 0.000000 2.000000 1.013024 -0.809881 4.000000 -0.177324 -0.797716 6.000000 -0.336553 1.026342 8.000000 0.862209 1.098934 10.000000 0.030590 -0.064096 12.000000 -1.120978 0.414704 14.000000 0.055131 0.539507 16.000000 0.538173 -1.159820 18.000000 -0.680319 -1.266793 20.000000 -0.100417 0.241133 Expected final conditions: 20.000000 -0.100418 0.241140 RK_TEST Problem number = 24 Runge-Kutta order = 3 Problem 24, Enright and Pryce #E4 The system is autonomous. Number of equations is 2 Stepsize H = 0.040000 0.000000 30.000000 0.000000 2.000000 30.063461 0.062930 4.000000 30.247711 0.119923 6.000000 30.536537 0.167090 8.000000 30.908719 0.203299 10.000000 31.343056 0.229523 12.000000 31.821464 0.247727 14.000000 32.330012 0.259992 16.000000 32.858666 0.268093 18.000000 33.400511 0.273372 20.000000 33.950914 0.276782 Expected final conditions: 20.000000 33.950914 0.276782 RK_TEST Problem number = 25 Runge-Kutta order = 3 Problem 25, Enright and Pryce #E5 The system is not autonomous. Number of equations is 2 Stepsize H = 0.040000 0.000000 0.000000 0.000000 2.000000 0.082270 0.083478 4.000000 0.339417 0.175238 6.000000 0.790461 0.277895 8.000000 1.460781 0.395294 10.000000 2.385320 0.533333 12.000000 3.614081 0.701538 14.000000 5.222257 0.916364 16.000000 7.330641 1.208889 18.000000 10.152071 1.645714 20.000000 14.117974 2.400000 Expected final conditions: 20.000000 14.117974 2.400000 RK_TEST Problem number = 26 Runge-Kutta order = 3 Problem 26, Enright and Pryce #F1 This problem has 1 parameters. The system is autonomous. Number of equations is 2 Stepsize H = 0.040000 0.000000 0.000000 0.000000 2.000000 -0.448455 0.028152 4.000000 -0.995919 0.062721 6.000000 -1.664251 0.105170 8.000000 -2.480136 0.157291 10.000000 -3.476151 0.221286 12.000000 -4.692065 0.299860 14.000000 -6.176425 0.396328 16.000000 -7.988500 0.514764 18.000000 -10.200641 0.660164 20.000000 -12.901174 0.838662 Expected final conditions: 20.000000 -12.944606 -0.000000 RK_TEST Problem number = 27 Runge-Kutta order = 3 Problem 27, Enright and Pryce #F2 The system is not autonomous. Number of equations is 1 Stepsize H = 0.040000 0.000000 110.000000 2.000000 75.155739 4.000000 70.440304 6.000000 69.802169 8.000000 69.715811 10.000000 69.704125 12.000000 69.702543 14.000000 69.702329 16.000000 69.702300 18.000000 69.702296 20.000000 69.702296 Expected final conditions: 20.000000 70.037311 RK_TEST Problem number = 28 Runge-Kutta order = 3 Problem 28, Enright and Pryce #F3 The system is autonomous. Number of equations is 2 Stepsize H = 0.040000 0.000000 0.000000 0.000000 2.000000 -0.922871 -0.593273 4.000000 -1.073067 0.495921 6.000000 -0.016234 0.183719 8.000000 -0.747730 -0.655802 10.000000 -1.203145 0.363351 12.000000 -0.084181 0.357691 14.000000 -0.559322 -0.666467 16.000000 -1.292296 0.197282 18.000000 -0.199765 0.507523 20.000000 -0.372714 -0.622981 Expected final conditions: 20.000000 -0.372696 -0.623014 RK_TEST Problem number = 29 Runge-Kutta order = 3 Problem 29, Enright and Pryce #F4 The system is not autonomous. Number of equations is 1 Stepsize H = 0.040000 0.000000 1.000000 2.000000 15.872563 4.000000 45.704287 6.000000 45.513810 8.000000 15.301134 10.000000 0.047619 12.000000 0.000144 14.000000 0.000003 16.000000 0.000000 18.000000 0.000000 20.000000 0.000000 Expected final conditions: 20.000000 0.000000 RK_TEST Problem number = 30 Runge-Kutta order = 3 Problem 30, Enright and Pryce #F5 The system is not autonomous. Number of equations is 1 Stepsize H = 0.040000 0.000000 1.000000 2.000000 0.801762 4.000000 0.672347 6.000000 0.591952 8.000000 0.548099 10.000000 0.534169 12.000000 0.548099 14.000000 0.591952 16.000000 0.672347 18.000000 0.801762 20.000000 1.000000 Expected final conditions: 20.000000 1.000000 RK_TEST Problem number = 31 Runge-Kutta order = 3 Problem 31, Lotka-Volterra Predator-Prey Equations. This problem has 4 parameters. The system is autonomous. Number of equations is 2 Stepsize H = 0.040000 0.000000 2.000000 2.000000 2.000000 1.098717 2.638929 4.000000 0.728547 3.722100 6.000000 0.651652 5.375933 8.000000 0.904382 7.705168 10.000000 2.202833 10.276221 12.000000 7.544768 9.860948 14.000000 12.452770 4.635025 16.000000 8.276401 2.215608 18.000000 4.182098 1.767158 20.000000 2.077727 1.974069 Expected final conditions: 20.000000 2.200500 10.272600 RK_TEST Problem number = 32 Runge-Kutta order = 3 Problem 32, The Lorenz System This problem has 3 parameters. The system is autonomous. Number of equations is 3 Stepsize H = 0.040000 0.000000 2.000000 2.000000 21.000000 2.000000 -14.060660 -11.852898 36.574016 4.000000 -0.893976 -1.582766 13.969692 6.000000 7.339115 -0.535846 33.868957 8.000000 5.488194 9.491602 13.418342 10.000000 4.179259 1.534824 26.172081 12.000000 7.243392 13.642289 10.686439 14.000000 -3.579897 -5.880163 14.158034 16.000000 9.044765 4.213012 32.874157 18.000000 13.789693 10.697754 36.993909 20.000000 1.473547 2.530763 14.020209 Expected final conditions: 20.000000 0.000000 0.000000 0.000000 RK_TEST Problem number = 33 Runge-Kutta order = 3 Problem 33, The Van der Pol equation This problem has 1 parameters. The system is autonomous. Number of equations is 2 Stepsize H = 0.040000 0.000000 2.000000 2.000000 2.000000 1.415956 -0.870930 4.000000 -1.969389 -0.504613 6.000000 -0.661781 1.478660 8.000000 1.859748 -0.518994 10.000000 -0.742405 -2.670765 12.000000 -1.401745 0.853029 14.000000 1.965206 0.504227 16.000000 0.654111 -1.486013 18.000000 -1.857016 0.521926 20.000000 0.756242 2.672941 Expected final conditions: 20.000000 0.756245 2.672940 RK_TEST Problem number = 34 Runge-Kutta order = 3 Problem 34, The Linearized Damped Pendulum This problem has 4 parameters. The system is autonomous. Number of equations is 2 Stepsize H = 0.040000 0.000000 2.000000 2.000000 2.000000 0.009634 4.261641 4.000000 -0.265830 0.572760 6.000000 -0.053717 -0.457522 8.000000 0.024991 -0.166906 10.000000 0.012120 0.028329 12.000000 -0.000955 0.027930 14.000000 -0.001811 0.001716 16.000000 -0.000229 -0.003400 18.000000 0.000197 -0.000900 20.000000 0.000070 0.000278 Expected final conditions: 20.000000 0.000070 0.000278 RK_TEST Problem number = 35 Runge-Kutta order = 3 Problem 35, The Nonlinear Damped Pendulum This problem has 4 parameters. The system is autonomous. Number of equations is 2 Stepsize H = 0.040000 0.000000 2.000000 2.000000 2.000000 -0.711979 0.669499 4.000000 -0.051058 -1.397305 6.000000 0.084934 -0.274295 8.000000 0.022808 0.134641 10.000000 -0.006888 0.063110 12.000000 -0.004410 -0.005586 14.000000 0.000052 -0.009550 16.000000 0.000601 -0.001136 18.000000 0.000111 0.001054 20.000000 -0.000058 0.000360 Expected final conditions: 20.000000 -0.000058 0.000360 RK_TEST Problem number = 36 Runge-Kutta order = 3 Problem 36, Duffing's Equation The system is autonomous. Number of equations is 2 Stepsize H = 0.200000 0.000000 0.500000 0.000000 10.000000 0.524362 -0.106288 20.000000 0.567459 -0.193397 30.000000 0.616057 -0.260842 40.000000 0.660470 -0.308371 50.000000 0.694393 -0.337064 60.000000 0.714553 -0.348928 70.000000 0.720138 -0.345884 80.000000 0.712233 -0.329050 90.000000 0.693445 -0.298695 100.000000 0.667713 -0.254718 Expected final conditions: 100.000000 0.667726 -0.254738 RK_TEST Problem number = 37 Runge-Kutta order = 3 Problem 37, Duffing's Equation with Damping and Forcing This problem has 3 parameters. The system is not autonomous. Number of equations is 2 Stepsize H = 0.200000 0.000000 0.500000 0.000000 10.000000 -1.429866 -0.403663 20.000000 -0.674260 -0.333633 30.000000 -0.937308 0.322004 40.000000 -0.310489 -0.225079 50.000000 -0.853308 -0.594415 60.000000 -0.041046 -0.200295 70.000000 0.097369 0.584763 80.000000 -0.278932 -0.668705 90.000000 0.884018 0.792964 100.000000 -1.175595 -0.586167 Expected final conditions: 100.000000 -1.217740 -0.548248 RK_TEST Problem number = 38 Runge-Kutta order = 3 Problem 38, Shampine's Ball of Flame This problem has 1 parameters. The system is autonomous. Number of equations is 1 Stepsize H = 0.400000 0.000000 0.010000 20.000000 0.012465 40.000000 0.016526 60.000000 0.024445 80.000000 0.046358 100.000000 0.275572 120.000000 1.000000 140.000000 1.000000 160.000000 1.000000 180.000000 1.000000 200.000000 1.000000 Expected final conditions: 200.000000 1.000000 RK_TEST Problem number = 39 Runge-Kutta order = 3 Problem 39, Polking's First Order System This problem has 2 parameters. The system is not autonomous. Number of equations is 1 Stepsize H = 0.018000 0.000000 0.500000 0.900000 0.309665 1.800000 -0.774323 2.700000 -1.490243 3.600000 -1.817307 4.500000 -2.061277 5.400000 -2.274842 6.300000 -2.468553 7.200000 -2.647336 8.100000 -2.814288 9.000000 -2.971540 Expected final conditions: 9.000000 -3.000000 RK_TEST Problem number = 40 Runge-Kutta order = 3 Problem 40, The Knee Problem This problem has 1 parameters. The system is not autonomous. Number of equations is 1 Stepsize H = 0.004000 -1.000000 -1.000000 -0.800000 -0.812137 -0.600000 -0.615848 -0.400000 -0.422561 -0.200000 -0.237322 0.000000 -0.079788 0.200000 -0.005525 0.400000 -0.000013 0.600000 -0.000000 0.800000 -0.000000 1.000000 -0.000000 Expected final conditions: 1.000000 -0.000000 TEST_ODE_TEST04 Create plots of ODE solutions. Saved plot of results in "p01.png" Saved plot of results in "p02.png" Saved plot of results in "p03.png" Saved plot of results in "p04.png" Saved plot of results in "p05.png" Saved plot of results in "p06.png" Saved plot of results in "p07.png" Saved plot of results in "p08.png" Saved plot of results in "p09.png" Saved plot of results in "p10.png" Saved plot of results in "p11.png" Saved plot of results in "p12.png" Saved plot of results in "p13.png" Saved plot of results in "p14.png" Saved plot of results in "p15.png" Saved plot of results in "p16.png" Saved plot of results in "p17.png" Saved plot of results in "p18.png" Saved plot of results in "p19.png" Saved plot of results in "p20.png" Saved plot of results in "p21.png" Saved plot of results in "p22.png" Saved plot of results in "p23.png" Saved plot of results in "p24.png" Saved plot of results in "p25.png" Saved plot of results in "p26.png" Saved plot of results in "p27.png" Saved plot of results in "p28.png" Saved plot of results in "p29.png" Saved plot of results in "p30.png" Saved plot of results in "p31.png" Saved plot of results in "p32.png" Saved plot of results in "p33.png" Saved plot of results in "p34.png" Saved plot of results in "p35.png" Saved plot of results in "p36.png" Saved plot of results in "p37.png" Saved plot of results in "p38.png" Saved plot of results in "p39.png" Saved plot of results in "p40.png" TEST_ODE_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 1.71788e-10 2 7.18127e-09 3 2.25671e-09 4 3.07386e-09 5 6.66682e-09 6 1.66806e-09 7 5.6679e-09 8 2.20514e-08 9 7.61029e-09 10 3.72946e-09 11 3.58786e-10 12 3.90557e-10 13 4.90515e-10 14 2.76843e-10 15 3.87371 16 1.73177e-07 17 2.14607e-07 18 9.29657e-08 19 5.333e-08 20 3.77543e-08 21 5.94267e-10 22 4.03525e-09 23 5.52285e-09 24 7.15264e-09 25 1.60574e-09 26 1.92524e-07 27 7.50702e-09 28 2.28894e-09 29 0 30 3.08031e-13 31 1.68546e-08 32 1.56892e-07 33 7.01863e-08 34 7.07587e-09 35 1.47085e-08 36 4.70444e-08 37 1.02067e-07 38 5.46645e-08 39 6.46321e-08 40 1.53088e-06 test_ode_test Normal end of execution. 30-Mar-2019 18:17:03