Exponentially fitted numerical method for solving singularly perturbed delay reaction-diffusion problem with nonlocal boundary condition

Abstract

Objectives: In this article, singularly perturbed delay reaction-diffusion problem with nonlocal boundary condition is considered. The exponential fitting factor is introduced to treat the solutions inside the boundary layer which occur due to perturbation parameter. The considered problem has interior layer at x = 1 and strong boundary layers at x = 0 and x = 2. We proposed an exponentially fitted finite difference method to solve the considered problem. The nonlocal boundary condition is treated using Composite Simpson’s 1/3 rule. Result: The stability and uniform convergence analysis of the proposed approach are established. The error estimation of the developed method is shown to be second-order uniform convergent. Two test examples are carried out to validate the applicability of the developed numerical method. The numerical results reflect the theoretical estimations. AMS Subject Classification: Primary 65L11, 65L12, 65L20, 65L70.