probnum.problems.zoo.diffeq.lorenz63(t0=0.0, tmax=20.0, y0=None, params=(10.0, 28.0, 2.6666666666666665))[source]

Initial value problem (IVP) based on the Lorenz63 system.

The Lorenz63 system is defined through

\[\begin{split}f(t, y) = \begin{pmatrix} a(y_2 - y_1) \\ y_1(b-y_3) - y_2 \\ y_1y_2 - cy_3 \end{pmatrix}\end{split}\]

for some parameters \((a, b, c)\). Default is \((a, b, c)=(10, 28, 2.667)\). This implementation includes the Jacobian \(J_f\) of \(f\).

  • t0 – Initial time.

  • tmax – Final time.

  • y0(shape=(3, )) – Initial value. Defaults to [0., 1., 1.05].

  • params – Parameters (a, b, c) of the Lorenz63 model.


InitialValueProblem object describing the Lorenz63 system with the prescribed configuration.

Return type