A Nonstandard Finite Difference Scheme for the Reaction Diffusion Equation

Abstract:

We use the nonstandard finite difference (NSFD) method to construct discrete models of the reaction diffusion equation. A nonstandard finite difference scheme for the reaction-diffusion equation is given. We demonstrated that the space denominator function can be based on the use of a transformation from the simple expression (Δx)²to an 4C(sin[(1/C)^1/2((Δx)/2)])².which is clearly valid for sufficiently small Δx. Another important class for which this method keeps the equation solutions are positivity and can be applied is those PDE's without advection term.

• Periodical: Applied Mechanics and Materials (Volumes 166-169)
• Pages: 3265-3268
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.166-169.3265
• Online since: May 2012
• Authors: Ming Ding Liu
• Keywords: Finite Difference Method (FDM), Nonstandard Finite Difference Scheme, Positivity, Reaction-Diffusion Equation

References

[1] R.E. Mickens, Determination of denominator functions for a NSFD scheme for the Fisher PDF with nonlinear advection, Math and Computers in Simulation.74 (2007)190-195.

DOI: 10.1016/j.matcom.2006.10.006

[2] R.E. Mickens, Nonstandard finite difference models of differential equations, World Scientific, Singapore, 1994.