An efficient algorithm for solving piecewise-smooth dynamical systems

Nicola Guglielmi; Ernst Hairer

doi:10.1007/s11075-021-01154-1

An efficient algorithm for solving piecewise-smooth dynamical systems

Numer Algorithms. 2022;89(3):1311-1334. doi: 10.1007/s11075-021-01154-1. Epub 2021 Jul 5.

Authors

Nicola Guglielmi¹, Ernst Hairer²

Affiliations

¹ Gran Sasso Science Institute, via Crispi 7, I-67100 L'Aquila, Italy.
² Section de Mathématiques, Université de Genève, rue du Conseil-Général 7-9, CH-1205 Genève, Switzerland.

Abstract

This article considers the numerical treatment of piecewise-smooth dynamical systems. Classical solutions as well as sliding modes up to codimension-2 are treated. An algorithm is presented that, in the case of non-uniqueness, selects a solution that is the formal limit solution of a regularized problem. The numerical solution of a regularized differential equation, which creates stiffness and often also high oscillations, is avoided.

Keywords: Codimension-2 manifold; Filippov solution; Hidden dynamics; Piecewise-smooth systems; Regularization; Scaling invariance.