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 - <p style="text-align: justify;">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.</p>