The Euler scheme for state constrained ordinary differential inclusions

TL;DR

This paper introduces a modified Euler scheme for solving state constrained differential inclusions, providing convergence analysis under weak assumptions and illustrating the results with a numerical example.

Contribution

It presents a novel variation of the Euler scheme tailored for state constrained differential inclusions with convergence proofs under minimal assumptions.

Findings

Convergence of the scheme is established for both space-continuous and space-discrete versions.

Numerical example demonstrates the practical applicability and interpretation of the convergence results.

Abstract

We propose and analyze a variation of the Euler scheme for state constrained ordinary differential inclusions under weak assumptions on the right-hand side and the state constraints. Convergence results are given for the space-continuous and the space-discrete versions of this scheme, and a numerical example illustrates in which sense these limits have to be interpreted.