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.