A TRIGONOMETRIC METHOD FOR THE LINEAR STOCHASTIC WAVE EQUATION

被引：60

作者：

Cohen, David ^{[1
]}

Larsson, Stig ^{[2
,3
]}

Sigg, Magdalena ^{[4
]}

机构：

[1] Karlsruher Inst Technol, Inst Angew & Numer Math, DE-76128 Karlsruhe, Germany

[2] Chalmers, Dept Math Sci, SE-41296 Gothenburg, Sweden

[3] Univ Gothenburg, SE-41296 Gothenburg, Sweden

[4] Univ Basel, Math Inst, CH-4051 Basel, Switzerland

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2013年 / 51卷 / 01期

基金：

瑞典研究理事会; 瑞士国家科学基金会;

关键词：

stochastic wave equation; additive noise; strong convergence; trace formula; stochastic trigonometric schemes; geometric numerical integration; PARTIAL-DIFFERENTIAL-EQUATIONS; EXPONENTIAL INTEGRATORS; ADDITIVE NOISE; APPROXIMATION; SCHEME;

D O I：

10.1137/12087030X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A fully discrete approximation of the linear stochastic wave equation driven by additive noise is presented. A standard finite element method is used for the spatial discretization and a stochastic trigonometric scheme for the temporal approximation. This explicit time integrator allows for error bounds independent of the space discretization and thus does not have a stepsize restriction as in the often used Stormer-Verlet-leap-frog scheme. Moreover, it enjoys a trace formula as does the exact solution of our problem. These favorable properties are demonstrated with numerical experiments.

引用

页码：204 / 222

页数：19

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