Geodesic
Error analysis of splitting methods for semilinear evolution equations
Applications of Mathematics, Tome 62 (2017) no. 4, pp. 405-432 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.21136/AM.2017.0020-17
Classification : 34B16, 34C25
Keywords: splitting method; semilinear evolution equations; error analysis 
@article{10_21136_AM_2017_0020_17,
     author = {Ohta, Masahito and Sasaki, Takiko},
     title = {Error analysis of splitting methods for semilinear evolution equations},
     journal = {Applications of Mathematics},
     pages = {405--432},
     year = {2017},
     volume = {62},
     number = {4},
     doi = {10.21136/AM.2017.0020-17},
     mrnumber = {3686424},
     zbl = {06770051},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.2017.0020-17/}
}
TY  - JOUR
AU  - Ohta, Masahito
AU  - Sasaki, Takiko
TI  - Error analysis of splitting methods for semilinear evolution equations
JO  - Applications of Mathematics
PY  - 2017
SP  - 405
EP  - 432
VL  - 62
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.2017.0020-17/
DO  - 10.21136/AM.2017.0020-17
LA  - en
ID  - 10_21136_AM_2017_0020_17
ER  - 
%0 Journal Article
%A Ohta, Masahito
%A Sasaki, Takiko
%T Error analysis of splitting methods for semilinear evolution equations
%J Applications of Mathematics
%D 2017
%P 405-432
%V 62
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.2017.0020-17/
%R 10.21136/AM.2017.0020-17
%G en
%F 10_21136_AM_2017_0020_17
Ohta, Masahito; Sasaki, Takiko. Error analysis of splitting methods for semilinear evolution equations. Applications of Mathematics, Tome 62 (2017) no. 4, pp. 405-432. doi: 10.21136/AM.2017.0020-17

Cité par Sources :