One-sided direct event location techniques in the numerical solution of discontinuous differential systems
type: Item
instance of: scholarly article
title: One-sided direct event location techniques in the numerical solution of discontinuous differential systems
zbMATH Open document ID: 1338.65181
published in: BIT
publication date: 2016-02-01T00:00:00Z
review text: In numerical integration of discontinuous systems of Filippov type, as those arising in control engineering, it is essential that the computed trajectory of the ordinary differential equation hits correctly the discontinuity manifold (to avoid, for instance, undesired numerical chattering phenomena). This paper proposes a technique for approaching the event manifold from one side in such a way that only a finite number of steps is required to hit it. The idea is to use a time reparametrization in the original system of differential equations and then use a Runge-Kutta (RK) scheme in the new formulation. Since RK methods preserve linear invariants, then the numerical trajectory automatically reaches exactly a planar manifold in a finite number of steps. This is also true for RK Gauss methods when the manifold is quadratic. In the general case, it is shown that the scheme can be made monotone for a sufficiently small step size. Numerical tests show that RK methods on the transformed problem give generally better results than in the original formulation.
reviewed by: Fernando Casas
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A36
Mathematics Subject Classification ID: 65L06
zbMATH DE Number: 6537627
zbMATH Keywords: event manifold
zbMATH Keywords: time reparametrization
zbMATH Keywords: Runge-Kutta methods
zbMATH Keywords: monotone integration
zbMATH Keywords: discontinuous system
zbMATH Keywords: Gauss method
zbMATH Keywords: numerical test
author: Luca Dieci
author: Luciano Lopez
MaRDI profile type: Publication
full work available at URL: s10543-014-0538-5
OpenAlex ID: W2048616285
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DOI: 10.1007/S10543-014-0538-5
description: scientific article; zbMATH DE number 6537627