Using generating functions to convert an implicit (3,3) finite difference method to an explicit form on diffusion equation with different boundary conditions

Kazem, S; Chadwick, EA; Hatam, A; Deghan, M

Abstract

In this article, our main goal is to develop an idea to convert an implicit (3,3) Ø-scheme finite difference method to an explicit form for both linear and nonlinear diffusion equations and also for nonlinear advection-diffusion equation with different boundary conditions. Accordingly, we assist power series generating functions which are a routine method in discrete mathematics. Also, the stability analysis of Ø–scheme to implement in nonlinear advection–diffusion equation has been investigated. Finally, the new approach has been implemented for Fisher, reaction–diffusion, Burgers and coupled Burgers equations as test problems to verify the ability and efficiency of the method proposed in this paper.

Citation

Kazem, S., Chadwick, E., Hatam, A., & Deghan, M. (2015). Using generating functions to convert an implicit (3,3) finite difference method to an explicit form on diffusion equation with different boundary conditions. Numerical Algorithms, 71(4), 827-854. https://doi.org/10.1007/s11075-015-0026-2

• Journal Article Type: Article
• Acceptance Date: Jul 3, 2015
• Online Publication Date: Sep 3, 2015
• Publication Date: Sep 3, 2015
• Deposit Date: Dec 1, 2015
• Journal: Numerical Algorithms
• Print ISSN: 1017-1398
• Electronic ISSN: 1572-9265
• Publisher: Springer Verlag
• Volume: 71
• Issue: 4
• Pages: 827-854
• DOI: https://doi.org/10.1007/s11075-015-0026-2
• Publisher URL: http://dx.doi.org/10.1007/s11075-015-0026-2
• Related Public URLs: http://link.springer.com/journal/11075