Exponentially fitted finite difference method for singularly perturbed delay differential equations with integral boundary condition

In this paper, exponentially fitted finite difference method for solving singularly perturbed delay differential equation with integral boundary condition is considered. To treat the integral boundary condition, Simpson’s rule is applied. The stability and parameter uniform convergence of the proposed method are proved. To validate the applicability of the scheme, two model problems are considered for numerical experimentation and solved for different values of the perturbation parameter,  and mesh size,  The numerical results are tabulated in terms of maximum absolute errors and rate of convergence and it is observed that the present method is more accurate and -uniformly convergent for  where the classical numerical methods fails to give good result and it also improves the results of the methods existing in the literature.