An hybrid initial value method for singularly perturbed delay differential equations with interior layers and weak boundary layer

Abstract

Abstract In this paper, an hybrid initial value method on Shishkin mesh is suggested to solve singularly perturbed boundary value problem for second order ordinary delay differential equation with discontinuous convection coefficient and source term. In this method, the original problem of solving the second order differential equation is reduced to solving four first order differential equations. Among the four first order differential equations, three of them are singularly perturbed differential equations without delay and other one is a regular differential equation with a delay term. The singularly perturbed differential equations are solved by the second order hybrid finite difference schemes, whereas the delay differential equation is solved by the improved Euler method. An error estimate is derived by using the supremum norm and it is of almost second order convergence. Numerical results are provided to illustrate the theoretical results.