A Non-Asymptotic Method For Singularly Perturbed Delay Differential Equations

Abstract

In this paper, a non-asymptotic method is presented for solving singularly perturbed delay differential equations whose solution exhibits a boundary layer behavior. The second order singularly perturbed delay differential equation is replaced by an asymptotically equivalent first order neutral type delay differential equation. Then, Simpson’s integration formula and linear interpolation are employed to get three term recurrence relation which is solved easily by Discrete Invariant Imbedding Algorithm. Some numerical examples are given to validate the computational efficiency of the proposed numerical scheme for various values of the delay and perturbation parameters. AMS Mathematics Subject Classification : 65L10. Key words and phrases : Singular perturbations, Delay differential equations, Boundary layer, Integration method, Delay parameter.