# vanderpol_jax¶

probnum.problems.zoo.diffeq.vanderpol_jax(t0=0.0, tmax=30, y0=None, params=10.0)[source]

Initial value problem (IVP) based on the Van der Pol Oscillator, implemented in jax.

This function implements the second-order Van-der-Pol Oscillator as a system of first-order ODEs. The Van der Pol Oscillator is defined as

$\begin{split}f(t, y) = \begin{pmatrix} y_2 \\ \mu \cdot (1 - y_1^2)y_2 - y_1 \end{pmatrix}\end{split}$

for a constant parameter $$\mu$$. $$\mu$$ determines the stiffness of the problem, where the larger $$\mu$$ is chosen, the more stiff the problem becomes. Default is $$\mu = 0.1$$. This implementation includes the Jacobian $$J_f$$ of $$f$$.

Parameters
• t0 (float) – Initial time point. Leftmost point of the integration domain.

• tmax (float) – Final time point. Rightmost point of the integration domain.

• y0 (np.ndarray,) – (shape=(2, )) – Initial value of the problem.

• params ((float), optional) – Parameter $$\mu$$ for the Van der Pol Equations Default is $$\mu=0.1$$.

Returns

IVP object describing the Van der Pol Oscillator IVP with the prescribed configuration.

Return type

IVP