Analysis of Exponential–Polynomial Single Step Method for Singularly Perturbed Delay Differential Equations

This research presents Exponential – Polynomial Single Step Method (EPSSM), which uses non-linear polynomial interpolating function to solve Singularly Perturbed Delay Differential Equations (SPPDDEs). The stability polynomial of the method is obtained. The Local Grid Search Algorithm termed LGSA is applied in determining the stability region. The efficiency of these methods is compared with the other two numerical methods, namely Runge-Kutta Method (RKM) and Rational Single Step Method (RSM) through two examples of Singularly Perturbed Delay Differential Equations (SPPDDEs).