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