Space Semi-Discretisations for a Stochastic Wave Equation

被引：0
作者：
Lluís Quer-Sardanyons
Marta Sanz-Solé
机构：
[1] Universitat de Barcelona,Facultat de Matemàtiques
来源：
Potential Analysis | 2006年 / 24卷
关键词：
stochastic partial differential equations; wave equation; discretisation schemes; 60H35; 60H15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study an approximation scheme for a nonlinear stochastic wave equation in one-dimensional space, driven by a spacetime white noise. The sequence of approximations is obtained by discretisation of the Laplacian operator. We prove Lp-convergence to the solution of the equation and determine the rate of convergence. As a corollary, almost sure convergence, uniformly in time and space, is also obtained. Finally, the speed of convergence is tested numerically.
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页码：303 / 332
页数：29
相关论文
共 39 条
[1]  
Bensoussan A.(1992)Approximation of some stochastic differential equations by the splitting-up method Appl. Math. Optim. 25 81-106
[2]  
Glowinski R.(1972)On barrier problems for the vibrating string Z. Wahrscheinlichkeitstheor. Verw. Geb. 22 13-24
[3]  
Rascanu A.(1988)Random nonlinear wave equations: Smoothness of the solutions Probab. Theory Related Fields 79 469-508
[4]  
Cabaña E.M.(2002)Numerical approximations of some linear stochastic partial differential equations driven by special additive noises SIAM J. Numer. Anal. 40 1421-1445
[5]  
Carmona R.(1988)Semi-discretization of stochastic partial differential equations on Stochastics 23 131-148
[6]  
Nualart D.(1996) by a finite element technique Bull. Aust. Math. Soc. 54 79-85
[7]  
Du Q.(1998)Time-discretized Garlekin approximations of parabolic SPDEs Potential Anal. 9 1-25
[8]  
Zhang T.(1999)Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space–time white noise I Potential Anal. 11 1-37
[9]  
Germani A.(2003)Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space–time white noise II Ann. Probab. 31 564-991
[10]  
Piccioni M.(2005)On the splitting-up method and stochastic partial differential equations Potential Anal. 23 99-134
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