Fitted Mesh Methods for the Numerical Solutions of Singularly Perturbed Problems

Abstract

ABSTRACT In the present thesis an attempt has been made to derive some simple and efficient numerical methods for solving singularly perturbed problems which are easy to implement and are not costly in terms of computer time also. It is observed that the numerical methods presented have been found to be efficient over the conventional methods and are at the same time, conceptually simple. We consider mainly the one dimensional singularly perturbed problems. Apart from the construction of methods, a full fledged theory for their convergence and error estimates is also presented. Numerical experiments are carried out extensively to support the theoretical results. The thesis consists of seven chapters.