The Method of Fundamental Solutions for Solving Convection-Diffusion Equations with Variable Coefficients
C.M. Fan 1*, C.S. Chen 1, J. Monroe 21 Department of Mathematics, University of Southern Mississippi, Hattiesburg, MS 39406, USA.
2 Department of Mathematics, Spring Hill College, Mobile, AL 36608, USA.
Received 06 October 2008; Accepted (in revised version) 06 January 2009
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 onestage 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.AMS subject classifications: 35J25, 65N35
Key words: Meshless method, method of fundamental solutions, particular solution, singular value decomposition, time-dependent partial differential equations.
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