A tension spline fitted numerical scheme for singularly perturbed reaction-diffusion problem with negative shift

Abstract

Objective The paper is focused on developing and analyzing a uniformly convergent numerical scheme for a singularly perturbed reaction-diffusion problem with a negative shift. The solution of such problem exhibits strong boundary layers at the two ends of the domain due to the influence of the perturbation parameter, and the term with negative shift causes interior layer. The rapidly changing behavior of the solution in the layers brings significant difficulties in solving the problem analytically. We have treated the problem by proposing a numerical scheme using the implicit Euler method in the temporal direction and a fitted tension spline method in the spatial direction with uniform meshes. Result Stability and uniform error estimates are investigated for the developed numerical scheme. The theoretical finding is demonstrated by numerical examples. It is obtained that the developed numerical scheme is uniformly convergent of order one in time and order two in space.

Accurate Computational Approach for Singularly Perturbed Burger-Huxley Equations

“…Basically, from the review of existing literature, we observe a good thing: the procedure to consider initial guesses to linearize the non-linear term, and higher-order numerical methods are preferred as they provide more accurate solutions with low computational cost so that they are efficient methods, [6][7][8][9]. Moreover, it is a recent and active research area in engineering and science fields that arises in various physical models including heat supply in the human head, the process of oxygen diffusion, the growth of some tumor types, and so on, [10][11][12][13][14][15][16][17].…”