A fully discrete approximation of the one-dimensional stochastic wave equation

被引：26

作者：

Cohen, David ^{[1
]}

Quer-Sardanyons, Lluis ^{[2
]}

机构：

[1] Umea Univ, Matemat & Matemat Stat, S-90187 Umea, Sweden

[2] Univ Autonoma Barcelona, Dept Matemat, Bellaterra 08193, Spain

来源：

IMA JOURNAL OF NUMERICAL ANALYSIS | 2016年 / 36卷 / 01期

基金：

瑞典研究理事会;

关键词：

nonlinear stochastic wave equation; multiplicative noise; strong convergence; finite differences; stochastic trigonometric methods; PARTIAL-DIFFERENTIAL-EQUATIONS; FINITE-ELEMENT METHODS; NUMERICAL APPROXIMATION; LATTICE APPROXIMATIONS; TIME; DISCRETIZATION; DRIVEN; SCHEME;

D O I：

10.1093/imanum/drv006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A fully discrete approximation of one-dimensional nonlinear stochastic wave equations driven by multiplicative noise is presented. A standard finite difference approximation is used in space and a stochastic trigonometric method is used for the temporal approximation. This explicit time integrator allows for error bounds in LP(Omega), uniformly in time and space, in such a way that the time discretization does not suffer from any kind of CFL-type step-size restriction. Moreover, uniform almost sure convergence of the numerical solution is also proved. Numerical experiments are presented and confirm the theoretical results.

引用

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页码：400 / 420

页数：21

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