A uniform numerical method for solving a singularly perturbed neutral delay differential equation

In this paper, we deal with a singularly perturbed neutral-type delay differential problem. To solve this problem numerically, we construct a novel difference scheme on a layer-adapted mesh with the finite difference method by using interpolated quadrature rules with remainder terms in integral form. We prove that this scheme is first-order uniformly convergent with respect to the small perturbation parameter in discrete maximum norm. We also present numerical experiments which confirm the theoretical findings.