This paper envisages the use of Liouville Green Transformation to find the solution of singularly perturbed delay differential equations. First, using Taylor series, the given singularly perturbed delay differential equation is approximated by an asymptotically equivalent singularly perturbation problem. Then the Liouville Green Transformation is applied to get the solution. The method is demonstrated by implementing several model examples by taking various values for the delay parameter and perturbation parameter.

In this paper, a numerical scheme is proposed to solve singularly perturbed differentialdifference equations with boundary layer behaviour using two fitting factor inserted at convective and diffusion terms. The singularly perturbed differential difference equation is replaced by an equivalent two point singularly perturbation problem. Then to handle the boundary layer, a two parameter fitted scheme is derived and it is applied to get the accurate solution. Model examples are solved using this approach and numerical results along with graphical representation are shown to support the method.

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