InternationaleJournals

A Computational Method For Solving Singularly Perturbed Initial Value Problems

K.Selva Kumar

Department of Mathematics, Anna University of  Technology, Tirunelveli - 627007,  Tamil Nadu, India.  E-mail: k_selvakumar10@yahoo.com

 

 

ABSTRACT                                                                 

              A computational method is presented for solving singularly perturbed initial  value problems with  an initial layer on the left end point of the interval. It is designed for  the practicing engineer or applied mathematician who needs a practical tool for these problems easy to use, modest  problem preparation and ready computer implementation.  The zeroth order asymptotic expansion is used to obtain the terminal boundary condition. Then, a  initial  layer region  and a non-initial layer region  are created.  And so, the given problem is  split  into two  initial  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 3, Issue 2, Pages:  1487 - 1501