ODE with non-differentiable RHS: "Filippov solver"?

Question

I've a differential system $\dot{x}=F(x)$ where $F:\mathbb{R}^d\to \mathbb{R}^d$ is bounded, non-differentiable on a countable set of points and Lipschitz elsewhere. This should imply that solutions (in the sense of Filippov) are absolutely continuous.

I'm looking for a software able to simulate these trajectories, as I noticed that Matlab, which works fine when F is Lipschitz, fails. Does anybody know what can I use to simulate this system?

Answer 1

Try DISODE45. The group of researchers have come up with a matlab function that helps you solve the problem you are describing and they have good documentation on how to use it as well.

Here's the link you might find useful.

https://iuma.unizar.es/es/investigacion/software/disode45

Disclaimer : I am not the author of this code and take no credit for it. I simply came across this while working on my own research and found it useful.