Error analysis of splitting methods for semilinear evolution equations

Masahito Ohta, Takiko Sasaki

Research output: Contribution to journalArticle

Abstract

We consider a Strang-type splitting method for an abstract semilinear evolution equation ∂tu=Au+F(u). Roughly speaking, the splitting method is a time-discretization approximation based on the decomposition of the operators A and F. Particularly, the Strang method is a popular splitting method and is known to be convergent at a second order rate for some particular ODEs and PDEs. Moreover, such estimates usually address the case of splitting the operator into two parts. In this paper, we consider the splitting method which is split into three parts and prove that our proposed method is convergent at a second order rate.

Original languageEnglish
Pages (from-to)405-432
Number of pages28
JournalApplications of Mathematics
Volume62
Issue number4
DOIs
Publication statusPublished - 2017 Aug 1
Externally publishedYes

Keywords

  • error analysis
  • semilinear evolution equations
  • splitting method

ASJC Scopus subject areas

  • Applied Mathematics

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