SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Contributed Talk

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Mean-square convergence order of a stochastic symplectic semi-discrete scheme for the stochastic Schrödinger equation

C. Chen and J. Hong

Abstract
A stochastic symplectic semi-discrete scheme in temporal direction is proposed for the stochastic Schrödinger equation in Stratonovich sense. To study its convergence order, a convergence theorem is presented. It establishes the relationship between the mean-square convergence order of a semi-discrete scheme and its local error. Based on it, we show that the semi-discrete scheme has mean-square order 1 under appropriate assumptions.

Bibliography
[1] A. De Bouard and A. Debussche, Weak and Strong order of convergence of a semidiscrete scheme for the stochastic nonlinear Schrödinger equation, Appl. Math. Optim., 54 (2006), pp. 369-399.
[2] S. S. Jiang, L. J. Wang and J. L. Hong, Stochastic Multi-symplectic integrator for stochastic Schrödinger equation, Commun. Comput. Phys., 14 (2014), pp. 393-411.
[3] G. Milstein and M. Tretyakov, Stochastic numerics for mathematical physics, Springer-Verlag Berlin Heidelberg, 2004.

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