Weak and strong order of convergence of a semidiscrete scheme for the stochastic nonlinear Schrodinger equation

被引：62
作者：
de Bouard, Anne [1 ]
Debussche, Arnaud
机构：
[1] Univ Paris 11, Math Lab, CNRS, F-91405 Orsay, France
[2] IRMAR, F-35170 Bruz, France
[3] ENS Cachan, Antenne Bretagne, F-35170 Bruz, France
来源：
APPLIED MATHEMATICS AND OPTIMIZATION | 2006年 / 54卷 / 03期
关键词：
nonlinear Schrodinger equations; stochastic partial differential equations; numerical schemes; rate of convergence;
D O I：
10.1007/s00245-006-0875-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article we analyze the error of a semidiscrete scheme for the stochastic nonlinear Schrodinger equation with power nonlinearity. We consider supercritical or subcritical nonlinearity and the equation can be either focusing or 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.
引用
收藏
页码：369 / 399
页数：31
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