Error analysis of splitting methods for semilinear evolution equations

@article{Ohta2017,
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.},
author = {Ohta, Masahito, Sasaki, Takiko},
journal = {Applications of Mathematics},
keywords = {splitting method; semilinear evolution equations; error analysis},
language = {eng},
number = {4},
pages = {405-432},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Error analysis of splitting methods for semilinear evolution equations},
url = {http://eudml.org/doc/294119},
volume = {62},
year = {2017},
}

TY - JOUR
AU - Ohta, Masahito
AU - Sasaki, Takiko
TI - Error analysis of splitting methods for semilinear evolution equations
JO - Applications of Mathematics
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 4
SP - 405
EP - 432
AB - 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.
LA - eng
KW - splitting method; semilinear evolution equations; error analysis
UR - http://eudml.org/doc/294119
ER -