Two-Dimensional Nonlinear Reaction Diffusion Equation with Time Efficient Scheme - American Journal of Computational Mathematics

AJCM > Vol.7 No.2, June 2017

American Journal of Computational Mathematics

Volume 7, Issue 2 (June 2017)

ISSN Print: 2161-1203 ISSN Online: 2161-1211

Google-based Impact Factor: 1.05 Citations

Two-Dimensional Nonlinear Reaction Diffusion Equation with Time Efficient Scheme ()

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Download as PDF (Size: 6066KB) PP. 183-194

DOI: 10.4236/ajcm.2017.72017 1,936 Downloads 5,548 Views Citations

Author(s)

Shahid Hasnain, Muhammad Saqib, Daoud Suleiman Mashat

Affiliation(s)

Department of Mathematics, Numerical Analysis, King Abdulaziz University, Jeddah, KSA.

ABSTRACT

This research paper represents a numerical approximation to non-linear two-dimensional reaction diffusion equation from population genetics. Since various initial and boundary value problems exist in two-dimensional reaction-diffusion, phenomena are studied numerically by different numerical methods, here we use finite difference schemes to approximate the solution. Accuracy is studied in term of L₂, L_∞ and relative error norms by random selected grids along time levels for comparison with exact results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. It is shown that the numerical schemes give better solutions. Moreover, the schemes can be easily applied to a wide class of higher dimension nonlinear reaction diffusion equations with a little modification.

KEYWORDS

Forward in Time and Centre in Space (FTCS), Taylor’s Series, Crank Nicolson, Alternating Direction Implicit (ADI) Scheme

Share and Cite:

Hasnain, S., Saqib, M. and Mashat, D.S. (2017) Two-Dimensional Nonlinear Reaction Diffusion Equation with Time Efficient Scheme. American Journal of Computational Mathematics, 7, 183-194. doi: 10.4236/ajcm.2017.72017.

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