vivyd.solvers.Midpoint

class Midpoint(verbose=False)

Bases: Solver

A midpoint integrator for solving systems of ordinary differential equations of the form

\[\dfrac{ds}{dt} = f(t, s).\]

The method is a second-order integrator that updates the state of the system at each time step as

\[\begin{split}t_{n+1/2} &= \dfrac{t_{n+1} + t_n}{2}, \\ s_{n+1/2} &= s_n + f(t_n, s_n) \cdot (t_{n+1/2} - t_n), \\ s_{n+1} &= s_n + f(t_{n+1/2}, s_{n+1/2}) \cdot (t_{n+1} - t_n).\end{split}\]

The integrator supports both pure Python and Taichi-accelerated implementations (as defined by the vivyd.models.TaichiCompatible and vivyd.models.TaichiConvertible protocols).

Parameters:

verbose (bool)