Applications of Mathematics

, Volume 62, Issue 4, pp 405–432

Error analysis of splitting methods for semilinear evolution equations

Article

Abstract

We consider a Strang-type splitting method for an abstract semilinear evolution equation
$${\partial _t}u = Au + F\left( u \right).$$
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.

Keywords

splitting method semilinear evolution equations error analysis 

MSC 2010

34B16 34C25 

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References

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2017

Authors and Affiliations

  1. 1.Department of MathematicsTokyo University of ScienceTokyoJapan
  2. 2.Department of MathematicsMeiji UniversityKanagawaJapan

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