1.3. Example: Solve van der Pol equation using Python

Let’s try using Open Interfaces by solving the Van der Pol equation:

\[ \frac{\mathrm d^2 x}{\mathrm d t^2} - \mu \left( 1 - x^{2} \right) \frac{\mathrm d x}{\mathrm d t} + x = 0, \quad x(0) = 2\]

with \(\mu = 1000\) using different implementations of the IVP interface (interface for solving initial-value problems for ordinary differential equations):

python examples/call_qeq_from_python.py [scipy_ode|sundials_cvode|jl_diffeq]

where the implementation argument is optional and defaults to scipy_ode.

This script uses stiff solvers for initial-value problems, why the value of the parameter \(\mu\) makes the system stiff. At the end of the computations, the resultant solution is displayed.