A robust uniformly convergent scheme for two parameters singularly perturbed parabolic problems with time delay

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 17 خرداد 1402   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2023.80721.1214

نویسنده

Naol Negero^*

Department of Mathematics, Wollega University, Nekemte, Ethiopia.

چکیده

A singularly perturbed time delay parabolic problem with two small parameters is considered. The paper develops a finite difference scheme that is exponentially fitted on a uniform mesh in the spatial direction and uses the implicit-Euler method to discretize the time derivative in the temporal direction in order to obtain a better numerical approximation to the solutions of this class of problems. We establish the parameter-uniform error estimate and discuss the stability of the suggested approach. In order to demonstrate the improvement in terms of accuracy, numerical results are also shown to validate the theoretical conclusions and are contrasted with the current hybrid scheme.

کلیدواژه‌ها

Singular perturbation؛ Two parameters parabolic convection-diffusion problem؛ time delay؛ Fitted operator scheme؛ the Error estimate