# Institute of Mathematics

## Error analysis of splitting methods for semilinear evolution equations

#### Masahito Ohta, Takiko Sasaki

###### Received January 30, 2017.  First published July 12, 2017.

Abstract:  We consider a Strang-type splitting method for an abstract semilinear evolution equation
\partial_t u = 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.
Keywords:  splitting method; semilinear evolution equations; error analysis
Classification MSC:  34B16, 34C25
DOI:  10.21136/AM.2017.0020-17

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Affiliations:   Masahito Ohta, Department of Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo, Japan; Takiko Sasaki, Department of Mathematics, Meiji University, 1-1-1 Higashimita Tama-ku, Kawasaki, Kanagawa, Japan, e-mail: takiko@meiji.ac.jp

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