Numerical Approximation to Nonlinear One Dimensional Coupled Reaction Diffusion System
| Autor: | Shahid Hasnain, Noorah Y. Mshary, Shafeek A. Ghaleb, Muhammad Saqib, D. S. Mashat |
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| Rok vydání: | 2017 |
| Předmět: |
010304 chemical physics
Mathematical analysis Finite difference 010103 numerical & computational mathematics 01 natural sciences Upper and lower bounds Nonlinear system Approximation error 0103 physical sciences Reaction–diffusion system Crank–Nicolson method Uniqueness 0101 mathematics Diffusion (business) Mathematics |
| Zdroj: | Journal of Applied Mathematics and Physics. :1551-1574 |
| ISSN: | 2327-4379 2327-4352 |
| DOI: | 10.4236/jamp.2017.58129 |
| Popis: | This research paper represents a numerical approximation to non-linear coupled one dimension reaction diffusion system, which includes the existence and uniqueness of the time dependent solution with upper and lower bounds of the solution. Also numerical approximation is obtained by finite difference schemes to reach at reasonable level of accuracy, which is magnified by L2, L∞ and relative error norms. The accuracy of the approximations is shown by randomly selected grid points along time level and comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Moreover, the schemes can be easily applied to a wide class of higher dimension non-linear reaction diffusion equations with a little modifications. |
| Databáze: | OpenAIRE |
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