Numerical solution of stochastic elliptic partial differential equations using the meshless method of radial basis functions

被引：30

作者：

Dehghan, Mehdi ^{[1
]}

Shirzadi, Mohammad ^{[1
]}

机构：

[1] Amirkabir Univ Technol, Dept Appl Math, Fac Math & Comp Sci, Tehran 15914, Iran

来源：

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS | 2015年 / 50卷

关键词：

Meshless method; Radial basis functions; Pseudospectral methods; Stochastic partial differential equations; Stochastic Laplace equation; Stochastic biharmonic equation; DATA APPROXIMATION SCHEME; COLLOCATION METHOD; DIFFUSION EQUATIONS; AMERICAN OPTIONS; ERROR ESTIMATE; MULTIQUADRICS; FORMULATION;

D O I：

10.1016/j.enganabound.2014.08.013

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, we propose two numerical methods to solve the elliptic stochastic partial differential equations (SPDEs) in two and three dimensions obtained by Gaussian noises using radial basis functions (RBEs) collocation and pseudospectral (PS) collocation methods. For approximating the solution, generalized inverse multiquadrics (GIMQ) RBFs have been used. The Gaussian noises are approximated at the collocation points. The schemes work in a similar fashion as Hermite-based interpolation methods. The methods are tested via several problems. The numerical results show usefulness and accuracy of the new methods. (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：291 / 303

页数：13

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