Fitted mesh numerical scheme for singularly perturbed delay reaction diffusion problem with integral boundary condition

This article presents a numerical treatment of the singularly perturbed delay reaction diffusion problem with an integral boundary condition. In the considered problem, a small parameter , is multiplied on the higher order derivative term. The presence of this parameter causes the existence of boundary layers in the solution. The solution also exhibits an interior layer because of the large spatial delay. Simpson’s 1/3 rule is applied to approximate the integral boundary condition given on the right end plane. A standard finite difference scheme on piecewise uniform Shishkin mesh is proposed to discretize the problem in the spatial direction, and the Crank-Nicolson method is used in the temporal direction. The developed numerical scheme is parameter uniformly convergent, with nearly two orders of convergence in space and two orders of convergence in time. Two numerical examples are considered to validate the theoretical results.