Spectral Method for Nonlinear Stochastic Partial Differential Equations of Elliptic Type

被引：2

作者：

Cao, Yanzhao ^{[2
]}

Yin, Li ^{[1
]}

机构：

[1] Inst Appl Phys & Computat Math, LCP, Beijing 100088, Peoples R China

[2] Auburn Univ, Dept Math, Auburn, AL 36849 USA

来源：

NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS | 2011年 / 4卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Stochastic differential equation; spectral method; error estimates; white noise; APPROXIMATION; DRIVEN; NOISE;

D O I：

10.4208/nmtma.2011.m99040

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the numerical approximations of semi-linear stochastic partial differential equations of elliptic type in multi-dimensions. Convergence analysis and error estimates are presented for the numerical solutions based on the spectral method. Numerical results demonstrate the good performance of the spectral method.

引用

页码：38 / 52

页数：15

共 20 条

[1]

Adams A., 2003, Sobolev Spaces, V140

[2]

Allen E. J., 1998, STOCH STOCH REP, V64, P117, DOI DOI 10.1080/17442509808834159

[3]

[Anonymous], STOCHAST STOCHAST RE

[4] Galerkin finite element approximations of stochastic elliptic partial differential equations [J].

Babuska, I ;

Tempone, R ;

Zouraris, GE .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2004, 42 (02) :800-825

[5]

BENTH EE, 1998, STOCHAST REP, V63, P313

[6]

BUCKDAHN R, 1989, DIFFUSION PROCESS RE, V1, P219

[7] Numerical approximation of some linear stochastic partial differential equations driven by special additive noises [J].

Du, Q ;

Zhang, TY .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2002, 40 (04) :1421-1445

[8]

GAO Y, 2006, STOCHASTICS, V78, P179

[9]

Gyngy I., 2006, Stoch. Int. J. Probab. Stoch. Process, V78, P213, DOI [10.1080/17442500600805047, DOI 10.1080/17442500600805047]

[10] Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise I [J].

Gyongy, I .

POTENTIAL ANALYSIS, 1998, 9 (01) :1-25

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