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https://doi.org/10.1007/BFb0070595

has been cited by the following article:

• TITLE: Two-Dimensional Nonlinear Reaction Diffusion Equation with Time Efficient Scheme

  AUTHORS: Shahid Hasnain, Muhammad Saqib, Daoud Suleiman Mashat

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

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.7 No.2, June 23, 2017

  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.