A mass-preserving splitting scheme for the stochastic Schrodinger equation with multiplicative noise

被引：12
|
作者：
Liu, Jie [1 ]
机构：
[1] Natl Univ Singapore, Dept Math, Singapore 119076, Singapore
来源：
IMA JOURNAL OF NUMERICAL ANALYSIS | 2013年 / 33卷 / 04期
关键词：
stochastic Schrodinger equation; splitting scheme; mass preserving; strong convergence; SEMIDISCRETE SCHEME;
D O I：
10.1093/imanum/drs051
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present a mass-preserving scheme for the stochastic nonlinear Schrodinger equation with multiplicative noise of Stratonovich type. It is a splitting scheme and we present an explicit formula for solving the sub-step related to the nonlinear part. The scheme is unconditionally stable in the L-2 norm. For the linear stochastic Schrodinger equation, we prove that the scheme has a strong convergence rate in time equal to 1, which is not common for stochastic partial differential equations with noise depending on space and time.
引用
收藏
页码：1469 / 1479
页数：11
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