Cimen, Erkan; Amiraliyev, Gabil M.

In this paper, we analyze a singularly perturbed convection-diffusion delay problem with Robin condition. In order to solve this problem numerically, we construct a fitted difference scheme on a uniform mesh. The scheme is based on the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with the weight and remainder terms in integral form. We prove that the method is first order convergence in the discrete maximum norm. Also, we present numerical results that support the theoretical results.

Amiraliyev, Gabil M.; Durmaz, Muhammet Enes; Kudu, Mustafa

The study deals with an initial-value problem for a singularly perturbed Fredholm integro-differential equation. Parameter explicit theoretical bounds on the continuous solution and its derivative are derived. Parameter uniform error estimates for the approximate solution are established. Numerical results are given to illustrate the parameter-uniform convergence of the numerical approximations.