—High order compact splitting method was applied for stochastic nonlinear Schrödinger equation. Using two-steps splitting method to decompose the original problem into a linear and nonlinear subproblem, then fourth-order compact difference scheme was applied to solve the linear part, while the nonlinear term was solved analytically. It is obvious to certify that the format, which we propose, is unconditional stable. What’s more, we give the expression of charge conservation law. Finally, numerical experiments were given to show forth order accuracy in space and we also observe the forms of solitary wave in the deterministic and stochastic case, which further reflected the superiority of this method.
—High order compact, two-steps splitting scheme, charge conservation law, energy conservation law.
The authors are with Beijing University of Chemical Technology, Beijing 100029, China (e-mail: email@example.com, firstname.lastname@example.org).
Cite: Zhaohui Dai and Shanshan Jiang, "High Order Compact Splitting Method for Stochastic Nonlinear Schrödinger Equation," International Journal of Modeling and Optimization vol. 4, no. 4, pp. 310-314, 2014.