A Simple Method of Numerical Integration for a Class of Singularly Perturbed Two Point Boundary Value Problems

Rakesh Ranjan*, H. S. Prasad**, Md. Javed Alam***
*,*** Research Scholar, Department of Mathematics, National Institute of Technology, Jamshedpur, Jharkhand, India.
** Assistant Professor, Department of Mathematics, National Institute of Technology, Jamshedpur, Jharkhand, India.
Periodicity:January - March'2018
DOI : https://doi.org/10.26634/jmat.7.1.14031

Abstract

This paper deals with a simple but efficient numerical integration method to solve a class of singularly perturbed twopoint boundary value problems. Using the methods of exact rule of integration with a finite difference approximation of first derivatives, a three-term recurrence relationship is obtained. The authors have employed Thomas algorithm to obtain the solution of the obtained system. Also, the stability and convergence of the proposed scheme are established. Several model example problems have been solved and the results are presented in terms of maximum absolute errors, which show the accuracy and efficiency of the method. The method produces highly accurate results for a fixed value of step size h when the perturbation parameter e tends to zero.

Keywords

Singular Perturbation Problems, Boundary Value Problems, Stability and Convergence, Simpson's Rule.

How to Cite this Article?

Rakesh Ranjan., H. S. Prasad., Md. Javed Alam. (2018). A Simple Method of Numerical Integration for A Class of Singularly Perturbed Two Point Boundary Value Problems. i-manager’s Journal on Mathematics, 7(1), 43-52. https://doi.org/10.26634/jmat.7.1.14031

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