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Accelerated fitted operator finite difference method for singularly perturbed parabolic reaction-diffusion problems | ||
| Computational Methods for Differential Equations | ||
| مقاله 18، دوره 9، شماره 3، مهر 2021، صفحه 886-898 اصل مقاله (550.77 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2020.39685.1737 | ||
| نویسندگان | ||
| Tesfaye Aga Bullo* 1؛ Gemechis File Duressa1؛ Guy Degla2 | ||
| 1Department of Mathematics, College of Natural science, Jimma University, Ethiopia. | ||
| 2Institut De Mathematiques et de sciences physiques, Universit D’Abomey Calavi, Benin. | ||
| چکیده | ||
| This paper deals with the numerical treatment of singularly perturbed parabolic reaction-diffusion initial boundary value problems. Introducing a fitting parameter into the asymptotic solution and applying average finite difference approximation, a fitted operator finite difference method is developed for solving the problem. To accelerate the rate of convergence of the method, Richardson extrapolation technique is applied. The consistency and stability of the proposed method have been established very well to ensure the convergence of the method. Numerical experimentation is carried out on some model problems and both the results are presented in tables and graphs. The numerical results are compared with findings of some methods existing in the literature and found to be more accurate. Generally, the formulated method is consistent, stable, and more accurate than some methods existing in the literature for solving singularly perturbed parabolic reaction-diffusion initial boundary value problems. | ||
| کلیدواژهها | ||
| Singularly perturbed parabolic problems؛ Reaction-diffusion؛ Fitted operator؛ Accurate solution | ||
| مراجع | ||
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