A Robust Numerical Scheme for Singularly Perturbed Delay Differential Equations with Turning Point

Abstract

In this article, we propose a parameter uniform numerical method for singularly perturbed delay differential equations with turning point. Using interpolation, a new algorithm is developed to tackle the retarded term. A fitted operator finite difference scheme using Il’in Allen Southwell fitting factor is used for numerical discretization. Bounds on the analytical solution and its derivatives are obtained. The efficiency of the proposed numerical method is illustrated via applying the proposed method on some test problems. The solution is proved to be stable and ε-uniform error estimates are derived. It is shown that the delay argument has significant effect on the solution behavior.

Keywords:

• Singular perturbation
• delay differential equation
• turning point problems
• fitted operator finite difference scheme
• convergence analysis