Numerical Solution of a Weakly Coupled System of Singularly Perturbed Delay Differential Equations Via Cubic Spline in Tension

In this paper, a fitted numerical scheme is proposed for solving coupled system of singularly perturbed convection-diffusion delay differential equations. Similar boundary value problems are associated with expected first exit times of the membrane potential in models of neurons. The difference scheme on uniform mesh is accomplished by the method which is based on cubic spline in tension. The difference scheme is shown to converge to the continuous solution uniformly with respect to the perturbation parameter, which is illustrated with numerical results.