A Uniform Convergent Method for Singularly Perturbed Nonlinear Differential-Difference Equation

Abstract

In this paper, the singularly perturbed boundary-value problem for a nonlinear second order delay differential equation is considered. For the numerical solution of this problem, we use an exponentially fitted difference scheme on a uniform mesh which is succeeded by the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with weight and remainder term in integral form. Also, the method is proved to be first-order convergent in the discrete maximum norm uniformly in the perturbation parameter. Furthermore, numerical illustration provide support of the theoretical results.