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

Abstract

Abstract Objectives In this article, a singularly perturbed delay reaction-diffusion problem with nonlocal boundary conditions 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 $$s = 1$$ s = 1 and strong boundary layers at $$s = 0$$ s = 0 and $$s= 2$$ s = 2 . We proposed an exponentially fitted finite difference method to solve the considered problem. The nonlocal boundary condition is treated using Composite Simpson’s $$\frac{1}{3}$$ 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 were carried out to validate the applicability of the developed numerical method. The numerical results reflect the theoretical estimations.

Keywords

• Singularly perturbed problem
• Reaction-diffusion problem
• Nonlocal boundary condition