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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.