van_der_pol_first_order

diffeqzoo.ivps.van_der_pol_first_order(**kwargs)

Construct the Van-der-Pol system as a first-order differential equation.

Warning

This problem has been generated by wrapping the function van_der_pol() through the function diffeqzoo.transform.second_to_first_order_auto().

The problem is not originally of first order. If you have access to solvers for second-order problems, it might be more efficient to solve the original problem.

The Van-der-Pol system is a non-conservative oscillator subject to non-linear damping. It is a popular benchmark problem, because it involves a parameter \(\mu\) (the “stiffness constant”) which governs the stiffness of the problem. For \(\mu ~ 1\), the problen is not stiff. For large values (e.g. \(\mu ~ 10^6\)) the problem is stiff. It was first published by Van der Pol (1920).

BibTex for Van der Pol (1920).

@article{van1920theory,
    title={Theory of the amplitude of free and forced triode vibrations},
    author={Van der Pol, Balthasar},
    journal={Radio Review},
    volume={1},
    pages={701--710},
    year={1920}
}