A Computational Method For Solving Singularly Perturbed Two Point Boundary Value Problems Without First Derivative Term
Department of Mathematics, Anna University of Technology Tirunelveli, Tirunelveli-627 007, Tamil Nadu, India
A computational method is presented for solving singularly perturbed two point boundary value problems without a first derivative term. The absence of first derivative term leads to the boundary layer regions nearer the end points of the interval(both left and right points of the interval). The solution of the reduced problem is used to obtain the terminal boundary conditions. Then, the two boundary layer regions and one non-boundary layer region are created. And so, the given problem is split into three two-point boundary value problems. All these problems are efficiently solved by an uniform and optimal exponentially fitted finite difference scheme. Error estimates for the computational method is derived using maximum principle,. Numerical results are given in this paper to demonstrate the applicability of the computational method.
Keywords: singular perturbation problems, exponentially fitted, uniformly convergent, asymptotic expansion, finite difference schemes.
AMS (MOS) Subject Classification: 65F05, 65N30, 65N35, 650Y05.
International eJournal of Mathematics and Engineering
Volume 1, Issue 4, Pages: 694 – 707