The Method of Fundamental Solutions for Solving Convection-Diffusion Equations with Variable Coefficients
Year: 2009
Author: C. M. Fan, C.S. Chen, J. Monroe
Advances in Applied Mathematics and Mechanics, Vol. 1 (2009), Iss. 2 : pp. 215–230
Abstract
A meshless method based on the method of fundamental solutions (MFS) is proposed to solve the time-dependent partial differential equations with variable coefficients. The proposed method combines the time discretization and the one-stage MFS for spatial discretization. In contrast to the traditional two-stage process, the one-stage MFS approach is capable of solving a broad spectrum of partial differential equations. The numerical implementation is simple since both closed-form approximate particular solution and fundamental solution are easier to find than the traditional approach. The numerical results show that the one-stage approach is robust and stable.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2009-AAMM-8365
Advances in Applied Mathematics and Mechanics, Vol. 1 (2009), Iss. 2 : pp. 215–230
Published online: 2009-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Meshless method method of fundamental solutions particular solution singular value decomposition time-dependent partial differential equations.