A mass-preserving splitting scheme for the stochastic Schrödinger equation with multiplicative noise (Q2856629)

A stochastic nonlinear Schrödinger equation with multiplicative noise of the form NEWLINE\[NEWLINE idu=\Delta u dt +V(x,|u|)udt+u\cdot dW,\;x\in \mathbb{R}^d, NEWLINE\]NEWLINE is considered, where \(u\cdot dW\) means the Stratonovich product. The author proposes a splitting scheme for an approximate solution of the equation which is mass-preserving at each step. At the sub-steps of the scheme connected with the nonlinear part an explicit solution for the corresponding equation is obtained. The strong convergence rate of the scheme is equal to 1 for linear equations.