Full Discretization of Stochastic Semilinear Schr\"odinger equation driven by multiplicative Wiener noise
Abstract
In this article, we have analyzed the full discretization of the Stochastic semilinear Schr\"odinger equation in a bounded convex polygonal domain driven by multiplicative Wiener noise. We use the finite element method for spatial discretization and the stochastic trigonometric method for time discretization and derive a strong convergence rate with respect to both parameters (temporal and spatial). Numerical experiments have also been performed to support theoretical bounds.
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