An initial-value technique to solve third-order reaction–diffusion singularly perturbed boundary-value problems

Abstract

The aim of this paper is to build an efficient initial-value technique for solving a third-order reaction–diffusion singularly perturbed boundary-value problem. Using this technique, a third-order reaction–diffusion singularly perturbed boundary-value problem is reduced to three approximate unperturbed initial-value problems and then Runge–Kutta fourth-order method is used to solve these unperturbed problems numerically.

Keywords:

• singular perturbation
• ordinary differential equations
• boundary-value problems

2010 AMS Subject Classification :

• 65N20

Acknowledgements

This research work has been financially supported by University Grant Commission (UGC), New Delhi, India, under sanctioned order number 37-515/2009(SR). The authors express their thanks to the reviewers for the valuable suggestions towards the improvement of the paper.