Numerical Integration Method for a Class of Singularly Perturbed Differential-Difference Equations

Abstract

In this paper a class of singularly perturbed differential-difference equation having boundary layer at one end is analysed to get its solution by numerical integration method. Taylor’s series expansion is applied on negative and positive shifts to get singularly perturbed differential equation. An asymptotically equivalent first order differential equation is obtained from SPDE using Taylor’s transformation. To integrate resulting equation, composite Simpson’s 1/3 rule is used to get three term recurrence relation. Thomas algorithm is used to get the solution of tridiagonal system of equations. Numerical solution obtained from this method approximates the available/exact solution very well.