Volume 1, Issue 2
The Method of Fundamental Solutions for Solving Convection-Diffusion Equations with Variable Coefficients

C.M. Fan ,  C.S. Chen and J. Monroe

Adv. Appl. Math. Mech., 1 (2009), pp. 215-230.

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  • 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 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.

  • History

Published online: 2009-01

  • AMS Subject Headings

35J25, 65N35

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