Fitted Parameter Exponential Spline Method for Singularly Perturbed Delay Differential Equations with a Large Delay

Abstract

In this paper, we present a new computational method based on an exponential spline for solving a class of delay differential equations with a negative shift in the differentiated term. When the shift parameter is O(ε), the proposed method works well and also controls the oscillations in the solution’s layer region. To accomplish this, we included a parameter in the proposed numerical scheme that is based on a special type of mesh, and the parameter is evaluated using the theory of singular perturbation. Maximum absolute errors and convergences of numerical solutions are tabulated to demonstrate the efficiency of the proposed computational method and to support the convergence analysis of the presented scheme.