Convergence of continuous approximations for discontinuous ODEs

Authors:
H. Schiller;M. Arnold
Affiliations:
Institut für Mathematik, Martin-Luther-Universität Halle-Wittenberg, Theodor-Lieser-Straíe 5, 06120 Halle, Germany;Institut für Mathematik, Martin-Luther-Universität Halle-Wittenberg, Theodor-Lieser-Straíe 5, 06120 Halle, Germany
Venue:
Applied Numerical Mathematics
Year:
2012

Citing 4
Cited 1

Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems

Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Rigid-Body Dynamics with Friction and Impact

SIAM Review
A Numerical Scheme for Impact Problems II: The Multidimensional Case

SIAM Journal on Numerical Analysis
Optimal control of systems with discontinuous differential equations

Numerische Mathematik

A comparison of Filippov sliding vector fields in codimension 2

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We investigate a regularisation technique for the solution of discontinuous ordinary differential equations. It is shown that the solutions obtained by the regularisation procedure converge uniformly to an appropriately defined analytical solution whenever the regularisation parameter @e goes to zero. Under reasonable conditions the convergence can be shown to be linear in @e. Moreover, we present numerical evidence that suggests that the conditions for linear convergence can be further relaxed.