The implicit Euler scheme for one-sided Lipschitz differential inclusions

Wolf-Jüergen Beyn; Janosch Rieger

doi:10.3934/dcdsb.2010.14.409

Article Contents

2010, Volume 14, Issue 2: 409-428. Doi: 10.3934/dcdsb.2010.14.409

This issue Previous Article Two-sided error estimates for the stochastic theta method Next Article Carrying an inverted pendulum on a bumpy road

The implicit Euler scheme for one-sided Lipschitz differential inclusions

Wolf-Jüergen Beyn^1, and
Janosch Rieger^1,

1.
Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld

Received: June 30, 2009

Revised: October 31, 2009

Published: August 2010

Abstract Related Papers Cited by

Abstract

We propose a set-valued version of the implicit Euler scheme for relaxed one-sided Lipschitz differential inclusions and prove that the defining implicit inclusions have a well-defined solution. Furthermore, we give a convergence analysis based on stability theorems, which shows that the set-valued implicit Euler method inherits all favourable stability properties from the single-valued scheme. The impact of spatial discretization is discussed, a fully discretized version of the scheme is analyzed, and a numerical example is given.

Keywords:

Mathematics Subject Classification: 34A60, 65L20.

Citation:

Article Metrics

HTML views() PDF downloads(107) Cited by(0)

The implicit Euler scheme for one-sided Lipschitz differential inclusions

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

The implicit Euler scheme for one-sided Lipschitz differential inclusions

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content