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

C. M. Fan, C.S. Chen & J. Monroe

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

Published online: 2009-01

Export citation
  • 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 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.

  • Keywords

Meshless method, method of fundamental solutions, particular solution, singular value decomposition, time-dependent partial differential equations.

  • AMS Subject Headings

35J25, 65N35

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{AAMM-1-215, author = {C. M. and Fan and and 20615 and and C. M. Fan and C.S. and Chen and and 20616 and and C.S. Chen and J. and Monroe and and 20617 and and J. Monroe}, title = {The Method of Fundamental Solutions for Solving Convection-Diffusion Equations with Variable Coefficients}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2009}, volume = {1}, number = {2}, pages = {215--230}, 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 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.

}, issn = {2075-1354}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aamm/8365.html} }
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.

C.M. Fan, C.S. Chen & J. Monroe. (1970). The Method of Fundamental Solutions for Solving Convection-Diffusion Equations with Variable Coefficients. Advances in Applied Mathematics and Mechanics. 1 (2). 215-230. doi:
Copy to clipboard
The citation has been copied to your clipboard