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| We construct a splitting method for a nonlinear one dimensional stochastic Schr{\"o}dinger equation with bounded domain and homogeneous Neumann boundaries conditions.
We approximate the solution of our problem by the sequence of solutions of two types of equations: one without stochastic integral term, but containing the Laplace operator and the
other one containing only the stochastic integral term. The two types of equations are connected to each other by their initial values. We prove that the solutions of these equations both converge strongly to the variational solution of the Schr{\"o}dinger equation. The idea of proof is based on $[1]$. \\ \\
References \\ \\
$[1]$ Grecksch, W., Lisei, H.: Approximation of Stochastic Nonlinear Equations of Schr{\"o}dinger Type by the splitting method. Stoch.Anal.Appl. 31: 314-335, 2013 |
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