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

Abstract

Objective: A numerical scheme is developed and analyzed for a singularly perturbed reaction-diffusion problem with a negative shift. The influence of the perturbation parameter exhibits boundary layers at the two ends of the domain, and the negative shift causes a strong interior layer. The rapidly changing behavior of the solution in the layers brings significant difficulties in solving the problem analytically. The problem is treated by proposing a numerical scheme using the implicit Euler method in the temporal direction and the spline tension method in the spatial direction with uniform meshes. Result: Error estimate is investigated for the developed numerical scheme. The scheme is demonstrated by numerical examples. The theoretical and numerical results show that the method is uniformly convergent. Mathematics Subject Classification: Primary 65M06; secondary 65M12, 65M15

Accurate Computational Approach for Singularly Perturbed Burger-Huxley Equations

“…Thus, researchers tried to develop different methods to solve these equations that served as a ground to get prior knowledge and the limitations of the existing methods. 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].…”