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
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
收藏
页码:204 / 222
页数:19
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