Fitted mesh numerical method for singularly perturbed delay differential turning point problems exhibiting boundary layers

Abstract

This paper is concerned with the numerical study of singularly perturbed boundary value problems for delay differential equations with a turning point. The fitted mesh technique is employed to generate a piecewise uniform mesh, condensed in the neighbourhood of the boundary layers. The difference scheme is shown to converge to the continuous solution uniformly with respect to the perturbation parameter. Some numerical experiments are carried out to illustrate, in practice, the result of convergence proved theoretically and demonstrate the effect of the delay argument and the coefficient of the delay term on the layer behaviour of the solution.

Keywords:

• delay differential equation
• singular perturbation
• turning point
• piecewise uniform mesh
• error estimates

2000 Mathematics Subject Classifications::

• 34K26
• 65L12
• 34K28

Acknowledgement

The first author thanks the Council for Scientific and Industrial Research, New Delhi, India, for providing financial support for this research.