ACCELERATED SPATIAL APPROXIMATIONS FOR TIME DISCRETIZED STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

被引：5

作者：

Hall, Eric Joseph ^{[1
]}

机构：

[1] Univ Edinburgh, Sch Math, Edinburgh EH9 3JZ, Midlothian, Scotland

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2012年 / 44卷 / 05期

关键词：

Richardson's method; finite differences; linear stochastic partial differential equations of parabolic type; Cauchy problem; NUMERICAL SCHEMES; CAUCHY-PROBLEM; CONVERGENCE; EXPANSION; ERROR;

D O I：

10.1137/12086412X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The present article investigates the convergence of a class of space-time discretization schemes for the Cauchy problem for linear parabolic stochastic partial differential equations defined on the whole space. Sufficient conditions are given for accelerating the convergence of the scheme with respect to the spatial approximation to higher order accuracy by an application of Richardson's method. This work extends the results of Gyongy and Krylov [SIAM J. Math. Anal., 42 (2010), pp. 2275-2296] to schemes that discretize in time as well as space.

引用

页码：3162 / 3185

页数：24

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