A novel explicit fully-discrete momentum-preserving scheme of damped nonlinear stochastic wave equation influenced by multiplicative space-time noise

In this paper, the evolution laws of global momentum and averaged global momentum for the damped nonlinear stochastic wave equation (DNSWE) influenced by multiplicative space-time noise are derived. We innovatively combine the second-order central finite difference method and discrete gradient method in space, and integrate the splitting method and Stormer-Verlet type method in time. Both the novel spatial semi-discrete scheme and fully-discrete scheme constructed in this way can successfully preserve the corresponding evolution laws for discrete global momentum and discrete averaged global momentum. Numerical experiments on DNSWE with cubic nonlinearity validate the theoretical results.