TY - JOUR T1 - The Method of Fundamental Solutions for Solving Convection-Diffusion Equations with Variable Coefficients AU - Fan , C. M. AU - Chen , C.S. AU - Monroe , J. JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 215 EP - 230 PY - 2009 DA - 2009/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/aamm/8365.html KW - Meshless method, method of fundamental solutions, particular solution, singular value decomposition, time-dependent partial differential equations. AB -

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