Stochastic Klein–Gordon–Schr？dinger (KGS) equations are important mathematical models and describe the interaction between scalar nucleons and neutral scalar mesons in the stochastic environment. In this paper, we propose novel structure-preserving schemes to numerically solve stochastic KGS equations with additive noise, which preserve averaged charge evolution law, averaged energy evolution law, symplecticity, and multi-symplecticity. By applying central difference, sine pseudo-spectral method, or finite element method in space and modifying finite difference in time, we present some charge and energy preserved fully-discrete schemes for the original system. In addition, combining the symplectic Runge-Kutta method in time and finite difference in space, we propose a class of multi-symplectic discretizations preserving the geometric structure of the stochastic KGS equation. Finally, numerical experiments confirm theoretical findings. 

Publication: 

Journal of Computational Physics, Volume 500, 1 March 2024, 112740 

http://dx.doi.org/10.1016/j.jcp.2023.112740 

Author: 

Jialin Hong 

Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China 

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China 

Email: hjl@lsec.cc.ac.cn 

Baohui Hou 

Department of Mathematics, Shanghai University, Shanghai 200444, PR China 

Liying Sun 

Academy for Multidisciplinary Studies, Capital Normal University, Beijing 100048, PR China 

Xiaojing Zhang 

Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China