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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 and 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 , pp. 1-28.

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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.

Item Type: Article
Schools: Schools > School of Computing, Science and Engineering
Journal or Publication Title: Numerical Algorithms
Publisher: Springer Verlag
ISSN: 1017-1398
Related URLs:
Funders: Non funded research
Depositing User: EA Chadwick
Date Deposited: 01 Dec 2015 14:27
Last Modified: 01 Dec 2015 14:27
URI: http://usir.salford.ac.uk/id/eprint/37235

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