assimulo.examples.radau5ode_vanderpol.run_example(with_plots=True)[source]

Example for the use of the implicit Euler method to solve Van der Pol’s equation

$\begin{split}\dot y_1 &= y_2 \\ \dot y_2 &= \mu ((1.-y_1^2) y_2-y_1)\end{split}$

with $$\mu= 10^6$$.

on return:

• exp_mod problem instance
• exp_sim solver instance

Final Run Statistics: Van der Pol (explicit)

Number of steps                                 : 241
Number of function evaluations                  : 2233
Number of Jacobian evaluations                  : 160
Number of function eval. due to Jacobian eval.  : 320
Number of error test failures                   : 7
Number of LU decompositions                     : 251

Solver options:

Tolerances (absolute)   : 0.0001
Tolerances (relative)   : 0.0001

Simulation interval    : 0.0 - 2.0 seconds.
Elapsed simulation time: 0.027811050415 seconds.
[[  2.00000000e+00  -6.00000000e-01]
[  2.00000000e+00  -6.00000000e-01]
[  1.99999994e+00  -6.17278784e-01]
[  1.99999988e+00  -6.30079232e-01]
[  1.99999963e+00  -6.55259070e-01]
[  1.99999937e+00  -6.63110060e-01]
[  1.99999893e+00  -6.66184062e-01]
[  1.99999824e+00  -6.66643419e-01]
[  1.99999689e+00  -6.66667566e-01]
[  1.99999283e+00  -6.66670497e-01]
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[  1.99979211e+00  -6.66782107e-01]
[  1.99836381e+00  -6.67576631e-01]
[  1.98687544e+00  -6.74048240e-01]
[  1.92233919e+00  -7.13232695e-01]
[  1.73960894e+00  -8.58528199e-01]
[  1.61050739e+00  -1.01051806e+00]
[  1.49788205e+00  -1.20441372e+00]
[  1.40980462e+00  -1.42756821e+00]
[  1.33626809e+00  -1.70090772e+00]
[  1.27704197e+00  -2.02433478e+00]
[  1.22813753e+00  -2.41600825e+00]
[  1.18790992e+00  -2.88926803e+00]
[  1.15463079e+00  -3.46533748e+00]
[  1.12709274e+00  -4.16870687e+00]
[  1.10432395e+00  -5.02930366e+00]
[  1.08550490e+00  -6.08502752e+00]
[  1.06994594e+00  -7.38473414e+00]
[  1.05734623e+00  -8.95056382e+00]
[  1.04432804e+00  -1.14925706e+01]
[  1.03636338e+00  -1.39262782e+01]
[  1.02985870e+00  -1.68420948e+01]
[  1.02357666e+00  -2.10852692e+01]
[  1.01852177e+00  -2.63425309e+01]
[  1.01502994e+00  -3.16436978e+01]
[  1.01229321e+00  -3.73168440e+01]
[  1.00973871e+00  -4.43764823e+01]
[  1.00736526e+00  -5.30718588e+01]
[  1.00518058e+00  -6.35326466e+01]
[  1.00307946e+00  -7.64802537e+01]
[  1.00101279e+00  -9.26676543e+01]
[  9.98938022e-01  -1.13078556e+02]
[  9.96817242e-01  -1.38983310e+02]
[  9.94613986e-01  -1.72033009e+02]
[  9.92291486e-01  -2.14377153e+02]
[  9.89811555e-01  -2.68812257e+02]
[  9.87133497e-01  -3.38976853e+02]
[  9.84213085e-01  -4.29605773e+02]
[  9.81001569e-01  -5.46861183e+02]
[  9.77444642e-01  -6.98764248e+02]
[  9.73481321e-01  -8.95758542e+02]
[  9.69042709e-01  -1.15144602e+03]
[  9.64050573e-01  -1.48354952e+03]
[  9.58415702e-01  -1.91517307e+03]
[  9.52035979e-01  -2.47645429e+03]
[  9.44794091e-01  -3.20673481e+03]
[  9.36554779e-01  -4.15741641e+03]
[  9.27161512e-01  -5.39572881e+03]
[  9.16432413e-01  -7.00971420e+03]
[  9.04155203e-01  -9.11484400e+03]
[  8.90080870e-01  -1.18628429e+04]
[  8.73915573e-01  -1.54535182e+04]
[  8.55310173e-01  -2.01507242e+04]
[  8.33846320e-01  -2.63041059e+04]
[  8.09017580e-01  -3.43790426e+04]
[  7.80203021e-01  -4.49985143e+04]
[  7.46628906e-01  -5.90028416e+04]
[  7.07310670e-01  -7.75373266e+04]
[  6.60960046e-01  -1.02185996e+05]
[  6.05825754e-01  -1.35187465e+05]
[  5.39393449e-01  -1.79813615e+05]
[  4.57743406e-01  -2.41122657e+05]
[  3.53882661e-01  -3.27785871e+05]
[  2.15398083e-01  -4.54828957e+05]
[  3.50845030e-03  -6.63386272e+05]
[ -1.66547398e-01  -8.31902080e+05]
[ -3.32737341e-01  -9.87341725e+05]
[ -5.27970620e-01  -1.14579712e+06]
[ -7.79605852e-01  -1.28854660e+06]
[ -1.04150721e+00  -1.33180557e+06]
[ -1.28576414e+00  -1.24411034e+06]
[ -1.46555156e+00  -1.08317652e+06]
[ -1.64501104e+00  -8.28058910e+05]
[ -1.76322050e+00  -6.02849415e+05]
[ -1.83144103e+00  -4.50663868e+05]
[ -1.89303026e+00  -2.98646770e+05]
[ -1.93605375e+00  -1.83961916e+05]
[ -1.96797286e+00  -9.42545835e+04]
[ -1.98171781e+00  -5.43934218e+04]
[ -1.98848930e+00  -3.44806025e+04]
[ -1.99303212e+00  -2.10193149e+04]
[ -1.99579106e+00  -1.28037452e+04]
[ -1.99744499e+00  -7.86399061e+03]
[ -1.99844983e+00  -4.85737169e+03]
[ -1.99906661e+00  -3.00979150e+03]
[ -1.99944728e+00  -1.86858750e+03]
[ -1.99968304e+00  -1.16139410e+03]
[ -1.99982936e+00  -7.22283273e+02]
[ -1.99992026e+00  -4.49300043e+02]
[ -1.99997677e+00  -2.79467401e+02]
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[ -2.00006848e+00  -8.61685836e-01]
[ -2.00006856e+00  -2.85004887e-01]
[ -2.00006858e+00   7.40762688e-02]
[ -2.00006855e+00   2.97664841e-01]
[ -2.00006849e+00   4.36884370e-01]
[ -2.00006837e+00   5.51504770e-01]
[ -2.00006822e+00   6.13953708e-01]
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[ -2.00006773e+00   6.61200137e-01]
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[ -1.94025778e+00   7.01819296e-01]
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[ -1.63394869e+00   9.78524216e-01]
[ -1.52522258e+00   1.14997297e+00]
[ -1.42812793e+00   1.37378309e+00]
[ -1.35260347e+00   1.63053879e+00]
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[ -1.23881908e+00   2.31692039e+00]
[ -1.19681185e+00   2.76800744e+00]
[ -1.16199165e+00   3.31765509e+00]
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[ -9.38366390e-01   3.93748850e+03]
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[ -3.77973849e-01   3.06921740e+05]
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[  1.54662931e+00   9.80312960e+05]
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[  1.96588506e+00   1.00257967e+05]
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[  1.98778385e+00   3.65774660e+04]
[  1.99259093e+00   2.23440985e+04]
[  1.99553048e+00   1.35948270e+04]
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[  1.99901102e+00   3.19020953e+03]
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[  1.99981963e+00   7.65332566e+02]
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[  2.00001307e+00   1.84135280e+02]
[  2.00003620e+00   1.14407450e+02]
[  2.00005057e+00   7.09878785e+01]
[  2.00005948e+00   4.39509906e+01]
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[  2.00006837e+00   1.66326144e+01]
[  2.00007044e+00   1.01051183e+01]
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[  2.00007317e+00   3.41644672e-01]
[  2.00007319e+00  -3.88059907e-02]
[  2.00007316e+00  -2.75701248e-01]
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[  2.00007300e+00  -5.43071184e-01]
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[  2.00007142e+00  -6.66538800e-01]
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[  1.95185675e+00  -6.94658146e-01]
[  1.81534967e+00  -7.90818914e-01]
[  1.70616260e+00  -8.92799206e-01]]


Note

Press [source] (to the top right) to view the example.