Numerical stability for nonlinear evolution equations

Petra Csomós, István Faragó, Imre Fekete

Research output: Contribution to journalArticle

Abstract

The paper deals with discretisation methods for nonlinear operator equations written as abstract nonlinear evolution equations. Brezis and Pazy showed that the solution of such problems is given by nonlinear semigroups whose theory was founded by Crandall and Liggett. By using the approximation theorem of Brezis and Pazy, we show the N-stability of the abstract nonlinear discrete problem for the implicit Euler method. Motivated by the rational approximation methods for linear semigroups, we propose a more general time discretisation method and prove its N-stability as well.

Original languageEnglish
Pages (from-to)2752-2761
Number of pages10
JournalComputers and Mathematics with Applications
Volume70
Issue number11
DOIs
Publication statusPublished - Dec 2015

Keywords

  • Nonlinear rational approximations
  • Nonlinear semigroups
  • Nonlinear stability

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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