Initial Value Method for Solving Second Order Singularly Perturbed Two Point Boundary Value Problems
Department of Mathematics , Anna University of Technology Tirunelveli, Tirunelveli—627 007, Tamil Nadu, India.
Abstract: Initial value method is presented for solving singularly perturbed two point boundary value problems . The presence of first derivative term leads to a boundary layer region nearer the left end point of the interval . In this method, the approximate solution is obtained by solving the reduced problem and an initial value problem associated with the given singularly perturbed problem numerically. The reduced problem is solved by Runge Kutta method of order four and the other initial value problem is solved by a stiff method(exponentially fitted method of Doolan et al.,) of order one. The method do not require the matrix inversion for the numerical convergence. The method presented in this paper is a modified form of the method of Gasparo and Macconi. The error estimates for the numerical convergence of the method of Gasparo and Macconi and the method presented in this paper are derived. Numerical results are given in this paper to demonstrate the applicability of the initial value method.Keywords: singular perturbation problems, exponentially fitted, uniformly convergent, asymptotic expansion, finite difference schemes, initial value method.
International eJournal of Mathematics and Engineering
Volume 2, Issue 2, Pages: 920 - 931