A Computational Method For Solving Singularly Perturbed Two Point Boundary Value Problems Without First Derivative Term


K. Selvakumar,

Department of   Mathematics, Anna University of Technology Tirunelveli, Tirunelveli-627 007, Tamil Nadu, India

 
ABSTRACT

            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