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 variablecoefficients. The proposed method combines the time discretization and the one-stageMFS 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 differentialequations. The numerical implementation is simple since both closed-formapproximate particular solution and fundamental solution are easier to find than thetraditional approach. The numerical results show that the one-stage approach isrobust and stable.