An exponentially fitted finite difference scheme for a class of singularly perturbed delay differential equations with large delays

Abstract

This paper deals with singularly perturbed boundary value problem for a linear second order delay differential equation. It is known that the classical numerical methods are not satisfactory when applied to solve singularly perturbed problems in delay differential equations. In this paper we present an exponentially fitted finite difference scheme to overcome the drawbacks of the corresponding classical counter parts. The stability of the scheme is investigated. The proposed scheme is analyzed for convergence. Several linear singularly perturbed delay differential equations have been solved and the numerical results are presented to support the theory.

Keywords

• Singular perturbations
• Boundary layer
• Delay differential equation
• Exponentially fitted finite difference method