Applied Mathematics & Information Sciences

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In this paper, we describe a computational method for singularly perturbed delay differential equations with layer or oscillatory behaviour. In general, the numerical solution of a second order boundary value problem will be more difficult than the numerical solution of the first order differential equation. Hence, it is preferable to convert the second order problem into first order problems. In this method, we first convert the second order singularly perturbed delay differential equation to first order neutral type delay differential equation and employ the Simpson rule. Then, we use the linear interpolation to get tridiagonal system which is solved easily by discrete invariant imbedding algorithm. Several model examples for various values of the delay parameter and perturbation parameter are solved and the computational results are presented. We also discuss the convergence of the method.

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