midpoint_adaptive, a Python code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method, relying on fsolve() to solve the implicit equation, and using an adaptive timestep.

### Languages:

midpoint_adaptive is available in a MATLAB version and a Python version.

### Related Data and codes:

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### Reference:

1. Catalin Trenchea, John Burkardt,
Refactorization of the midpoint rule,
Applied Mathematics Letters,
Volume 107, September 2020.

### Source Code:

Last revised on 26 May 2022.