Geodesic
Long-time convergence of numerical approximations for 2D GBBM equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 3

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

We study the long-time behavior of the finite difference solution to the generalized BBM equation in two space dimensions with dirichlet boundary conditions. The unique solvability of numerical solution is shown. It is proved that there exists a global attractor of the discrete dynamical system. Finally, we obtain the long-time stability and convergence of the difference scheme. Our results show that the difference scheme can effectively simulate the infinite dimensional dynamical systems. Numerical experiment results show that the theory is accurate and the schemes are efficient and reliable. 
@article{ZVMMF_2016_56_3_a10,
     author = {Shuguang Li and Jue Wang},
     title = {Long-time convergence of numerical approximations for {2D} {GBBM} equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {441},
     publisher = {mathdoc},
     volume = {56},
     number = {3},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_3_a10/}
}
TY  - JOUR
AU  - Shuguang Li
AU  - Jue Wang
TI  - Long-time convergence of numerical approximations for 2D GBBM equation
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2016
SP  - 441
VL  - 56
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_3_a10/
LA  - en
ID  - ZVMMF_2016_56_3_a10
ER  - 
%0 Journal Article
%A Shuguang Li
%A Jue Wang
%T Long-time convergence of numerical approximations for 2D GBBM equation
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2016
%P 441
%V 56
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_3_a10/
%G en
%F ZVMMF_2016_56_3_a10
Shuguang Li; Jue Wang. Long-time convergence of numerical approximations for 2D GBBM equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 3. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_3_a10/