EXPONENTIALLY FITTED FINITE DIFFERENCE SCHEME FOR SOLVING SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS WITH SMALL AND LARGE DELAYS

Abstract

The main objective of this project is to study exponentially fitted finite difference method, develop stable, convergent and demonstrate the efficient numerical method for solving singularly perturbed differential equations having both small and large delay. The terms containing the delay parameters in the first derivative are approximated using Taylor series approximations resulting to asymptotically equivalent singularly perturbed boundary value problem. The singularly perturbed differential-difference equation are reduced or replaced by second order singularly perturbed delay differential equation with large delay have containing in first term. The numerical scheme is developed on uniform mesh using fitted finite operator in the given differential equation. The stability of the developed numerical methods is established and its uniform convergence of the scheme is proved. five linear singularly perturbed delay differential equations have been solved and the numerical results are presented to support the theory and plotted the graphs of the solution of the problem. On the basis of the numerical results of a variety of examples, it is concluded that the present method offers significant advantage for the linear singularly perturbed differential difference equations.