**InternationaleJournals**

**A Numerical technique for
Solving Singularly Perturbed Two Point Boundary Value Problems**

**N.
Raji Reddy ^{1}, J. Sucharitha^{2}**

^{1}Dept
of Mathematics Jyothishmathi Institute of Technology & Science, Karimnagar-505481, Andhra Pradesh, India.

^{2}Dept
of Mathematics, Osmania University, Hyderabad- 500007,
Andhra Pradesh, India.

**Abstract**

This paper discusses the solving of singularly perturbed two-point boundary value problems. It consists of replacing the original differential equation by a pair of initial value problems. Then first initial value problem (IVP) is solved in general way and then using the solution of this, solve second initial value problem with introducing exponential fitted finite difference scheme. Several linear and non-linear singular perturbation problems have been solved and the numerical results are presented to support the theory. It is observed that the present method approximates the exact solution very well.

**Keywords**: Ordinary
differential equations; Singular perturbations; Two Point Boundary value
problems; Initial value methods; Boundary layer,
exponentially fitted finite difference scheme.

**International
eJournal of Mathematics and Engineering**

**Volume 3,
Issue ****3,** **Pages: 1613 - 1623**