Parameter Fitted Scheme for Singularly Perturbed Delay Differential Equations

Abstract

In this paper, we presented a parameter fitted scheme to solve singularly perturbed delay differential equations of second order with left and right boundary. In this technique, approximating the term containing negative shift by Taylor series, we modified the singularly perturbed delay differential equations. We introduced a fitting parameter on the highest order derivative term of the modified problem. The fitting parameter is to be determined from the scheme using the theory of singular Perturbation. Finally, we obtained a three term recurrence relation that can be solved using Thomas algorithm. The applicability of the method is tested by considering four linear problems (two problems on left layer and two problems on right layer). It is observed that when the delay parameter is smaller than the perturbation parameter, the layer behavior is maintained.