Numerical Method For Solving Singularly Perturbed two parameter Delay Differential Equation using Non-standard Finite Difference Method

Abstract

Due to the wider applications of singularly perturbed differential equation (SPDDEs) in the real life problems, there has been growing interest to develop numerical methods for SPDDEs. However, as the perturbation parameter decreases in magnitude, standard numerical methods for solving singularly perturbed differential equations are unstable, inefficient and inaccurate. Thus, it is pretty reasonable to construct numerical meth ods whose convergence properties, accuracy and the computation cost are independent of the value of the perturbation parameter. One of the approaches to derive-uniform convergent numerical methods for solving SPDDEs is through the application of fitted op erator method which can be constructed by using either exponentially fitted operator or non-standard finite difference methods. The design of the non-standard finite difference methods (NSFDMs) starts mostly with the concept of exact schemes. A major advantage of having an exact difference scheme for a differential equation is that questions related to the usual considerations of consistency, stability and convergence do not arise. The objective of this project is, therefore, to construct-uniform convergent non-standard finite difference method for solving singularly perturbed two parameter delay differential equa tion using finite difference method. The convergence analysis and stability of the proposed method will also be established.