Rosenbrock-type methods applied to discontinuous differential systems

TL;DR

This paper explores the application of Rosenbrock methods to solve discontinuous differential systems, introducing a continuous extension technique for event detection and addressing singular perturbations.

Contribution

It presents a novel approach combining Rosenbrock schemes with continuous extensions for discontinuous and singularly perturbed systems.

Findings

Effective event point localization using continuous extension.

Successful application to discontinuous singularly perturbed systems.

Enhanced numerical solution accuracy for complex systems.

Abstract

In this paper we will study the numerical solution of a discontinuous differential system by a Rosenbrock method. We will also focus on one-sided approach in the context of Rosenbrock schemes, and we will suggest a technique based on the use of continuous extension, in order to locate the event point, with an application to discontinuous singularly perturbed systems.