American Journal of Computational Mathematics

Volume 7, Issue 2 (June 2017)

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

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Two-Dimensional Nonlinear Reaction Diffusion Equation with Time Efficient Scheme

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DOI: 10.4236/ajcm.2017.72017    1,184 Downloads   2,411 Views   Citations

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.

Cite this paper

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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