Quadrature method with exponential fitting for delay differential equations having Layer behavior

Abstract

In this paper, we suggest a computational method for solving delay differential equations, with one end layer, dual layer and interior layer behavior using Gaussian quadrature. The problem is initially replaced with the analogous first order neutral type delay differential equation by taking the perturbation parameter within the differentiated term. For the numerical solution with boundary layer at one endpoint, dual boundary layers and internal boundary layers, the Gaussian two-point quadrature scheme was extracted with exponential fitting. Using model examples, the suggested approach is used for various perturbation and delay parameter values. The numerical scheme is validated and supported by the comparison of maximum errors with the other results in the literature. Convergence of the method is examined. For various delay parameter values, the layer structure is depicted in graphs.