A fast mass-conserving explicit splitting method for the stochastic space-fractional nonlinear Schrödinger equation with multiplicative noise

Abstract A fast mass-conserving explicit splitting method is proposed to solve the stochastic space-fractional nonlinear Schrodinger equation which includes a nonlinear term, a fractional Laplacian term and a multiplicative noise term resulting from the nonlocal property, the random variation of the media and the exterior random disturbance. The method splits the original equation into two sub-equations so that appropriate numerical methods can be applied to each sub-equation. A variety of numerical examples in both one- and multi-dimensional spaces show that the scheme has good mass conservative property, first-order strong convergence in time and high efficiency.