The Method of Fundamental Solutions for Solving Convection-Diffusion Equations with Variable Coefficients
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.
Advances In Applied Mathematics and Mechanics
(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: http://aquila.usm.edu/fac_pubs/1146