The Method of Fundamental Solutions for Solving Convection-Diffusion Equations with Variable Coefficients

Authors

Chia-Ming Fan, National Taiwan Ocean UniversityFollow
Ching-Shyang Chen, University of Southern MississippiFollow
Jeannette Monroe, University of Southern Mississippi

Document Type

Article

Publication Date

4-1-2009

Department

Mathematics

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 easy to find than the traditional approach. The numerical results show that the one-stage approach is robust and stable.

Publication Title

Advances In Applied Mathematics and Mechanics

Volume

1

Issue

2

First Page

215

Last Page

230

Recommended Citation

Fan, C., Chen, C., Monroe, J. (2009). The Method of Fundamental Solutions for Solving Convection-Diffusion Equations with Variable Coefficients. Advances In Applied Mathematics and Mechanics, 1(2), 215-230.
Available at: https://aquila.usm.edu/fac_pubs/1146