Geodesic
New fourth-order splitting methods for two-dimensional evolution equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 4, pp. 696-699 
N. V. Shirobokov. New fourth-order splitting methods for two-dimensional evolution equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 4, pp. 696-699. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_4_a10/
@article{ZVMMF_2009_49_4_a10,
     author = {N. V. Shirobokov},
     title = {New fourth-order splitting methods for two-dimensional evolution equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {696--699},
     year = {2009},
     volume = {49},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_4_a10/}
}
TY  - JOUR
AU  - N. V. Shirobokov
TI  - New fourth-order splitting methods for two-dimensional evolution equations
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2009
SP  - 696
EP  - 699
VL  - 49
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_4_a10/
LA  - ru
ID  - ZVMMF_2009_49_4_a10
ER  - 
%0 Journal Article
%A N. V. Shirobokov
%T New fourth-order splitting methods for two-dimensional evolution equations
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2009
%P 696-699
%V 49
%N 4
%U http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_4_a10/
%G ru
%F ZVMMF_2009_49_4_a10

Voir la notice de l'article provenant de la source Math-Net.Ru

New second- and third-order splitting methods are proposed for partial differential equations of the evolution type in a two-dimensional space. The methods are derived as based on diagonal implicit techniques used in the numerical solution to stiff ordinary differential equations. The methods are absolutely and unconditionally stable. Test computations are presented.

[1] Dekker K., Verver Ya., Ustoichivost metodov Runge–Kutty dlya zhestkikh nelineinykh differentsialnykh uravnenii, Mir, M., 1988 | MR

[2] Shirobokov N. V., “Diagonalno-neyavnye skhemy Runge–Kutty”, Zh. vychisl. matem. i matem. fiz., 42:7 (2002), 1013–1018 | MR | Zbl

[3] Shirobokov N. V., “Novye metody rasschepleniya dlya dvumernykh evolyutsionnykh uravnenii”, Zh. vychisl. matem. i matem. fiz., 47:7 (2007), 1187–1191 | MR

[4] Marchuk G. I., Osnovy vychislitelnoi matematiki, Nauka, M., 1980 | MR