Exponentially fitted cubic spline for two-parameter singularly perturbed boundary value problems

Abstract

In this paper, we derive an exponentially fitted difference scheme using cubic splines for a singularly perturbed ordinary differential equation with two small parameters affecting the convection and diffusion terms. The solution of the problem exhibits a boundary layer on the left-hand side of the domain. Bounds on the derivatives of the solution are derived. A first-order numerical method is constructed. Numerical results are presented to establish the theoretical results and to show the efficiency of the method.

Keywords:

• singular perturbations
• two parameters
• fitted operator methods
• cubic splines

AMS Subject Classifications :

• 65L10
• 65L11
• 65D07

Acknowledgements

The authors are grateful to the anonymous referees and the editorial board for their valuable comments and suggestions that have led to an improved version of the article.