**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 zero^{th} 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**