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

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  • 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

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@Article{AAMM-1-215, author = {Fan , C. M. and Chen , C.S. and Monroe , J.}, 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:
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