Nonstandard finite difference method for solving Second order singularly perturbed problem having Large delay

Abstract

In this thesis, nonstandard fitted finite difference method has been presented for the numerical solution of a second order singularly perturbed problems having large delay. The behavior of the continuous solution of the problem is studied and shown that it satisfies the continuous stability estimate and the derivatives are also bounded. The numerical scheme is developed on a uniform mesh using non standard finite difference method. To validate the applicability of the method, one model problem is considered for numerical experimentation for different values perturbation parameter and mesh points. The method is shown to be ε-uniformly convergent with order of convergence O(h). The proposed method gives more accurate and ε-uniform numerical result.