The implicit Euler scheme for one-sided Lipschitz differential inclusions

Wolf Juergen Beyn, J. Rieger

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19 Citations (Scopus)


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 setvalued 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.

Original languageEnglish
Pages (from-to)409-428
Number of pages20
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number2
Publication statusPublished - 1 Sep 2010
Externally publishedYes


  • Differential inclusions
  • Implicit euler method
  • Numerical analysis

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