Weak and Strong Order of Convergence of a Semi Discrete Scheme for the Stochastic Nonlinear Schrödinger Equation
نویسنده
چکیده
In this article, we analyze the error of a semi discrete scheme for the stochastic non linear Schrödinger equation with power nonlinearity. We consider supercritical or subcritical nonlinearity and the equation can be either focusing of defocusing. Allowing sufficient spatial regularity we prove that the numerical scheme has strong order 1/2 in general and order 1 if the noise is additive. Furthermore, we also prove that the weak order is always 1.
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