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

N. Raji Reddy1, J. Sucharitha2

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

2Dept 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