Two-Dimensional Nonlinear Reaction Diffusion Equation with Time Efficient Scheme
| Autor: | Muhammad Saqib, Shahid Hasnain, D. S. Mashat |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
010302 applied physics
Numerical analysis Mathematical analysis Finite difference Von Neumann stability analysis 02 engineering and technology General Medicine 021001 nanoscience & nanotechnology 01 natural sciences Nonlinear system Approximation error 0103 physical sciences Reaction–diffusion system Crank–Nicolson method Boundary value problem 0210 nano-technology Mathematics |
| Zdroj: | American Journal of Computational Mathematics. :183-194 |
| ISSN: | 2161-1211 2161-1203 |
| DOI: | 10.4236/ajcm.2017.72017 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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