Uniformly convergent fitted operator method for singularly perturbed delay differential equations

Abstract

This paper deals with numerical treatment of singularly perturbed delay differential equations having delay on first derivative term. The solution of the considered problem exhibits boundary layer behaviour on left or right side of the domain depending on the sign of the convective term. The term with the delay is approximated using Taylor series approximation, resulting to asymptotically equivalent singularly perturbed boundary value problem. Uniformly convergent numerical scheme is developed using exponentially fitted finite difference method. The stability of the scheme is investigated using solution bound. The uniform convergence of the scheme is discussed and proved. Numerical examples are considered to validate the theoretical analysis.