TY - JOUR
T1 - Stochastic Global Momentum-Preserving Schemes for Two-Dimensional Stochastic Partial Differential Equations
AU - Song , Mingzhan
AU - Song , Songhe
AU - Zhang , Wei
AU - Qian , Xu
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 912
EP - 927
PY - 2022
DA - 2022/08
SN - 12
DO - http://doi.org/10.4208/eajam.110122.040522
UR - https://global-sci.org/intro/article_detail/eajam/20890.html
KW - Stochastic global momentum-preserving scheme, stochastic nonlinear Schrödinger equation, global momentum conservation law, stochastic Klein-Gordon equation, global momentum evolution law.
AB - <p style="text-align: justify;">In this paper, the global momentum conservation laws and the global momentum evolution laws are presented for the two-dimensional stochastic nonlinear Schrödinger equation with multiplicative noise and the two-dimensional stochastic Klein-Gordon
equation with additive noise, respectively. In order to preserve the global momenta or
their changing trends in numerical simulation, the schemes are constructed by using a
stochastic multi-symplectic formulation. It is shown that under periodic boundary conditions, the schemes have discrete global momentum conservation laws or the discrete
global momentum evolution laws. Numerical experiments confirm global momentum-preserving properties of the schemes and their mean square convergence in the time
direction.</p>