Solution of Singularly Perturbed Delay Differential Equations with Dual Layer Behaviour using Numerical Integration

In this paper, we proposed a numerical integration method for the solution of singularly perturbed delay differential equation with dual layer behaviour. In this method, an asymptotically equivalent first order neutral type delay differential equation is obtained from the second order singularly perturbed delay differential equation and employed Trapezoidal rule on it. Then, linear interpolation is used to get three term recurrence relation which is solved by discrete invariant imbedding algorithm. Numerical illustrations for various values of the delay parameter and perturbation parameter are presented to validate the proposed method. Convergence of the proposed method is also analyzed. Key–Words: Singularly perturbed delay differential equations, Dual layer, Exponential Integrating Factor, Numerical Integration