An ε-uniform numerical method for third order singularly perturbed delay differential equations with discontinuous convection coefficient and source term

A class of third order singularly perturbed Boundary Value Problems (BVPs) for ordinary delay differential equations with discontinuous convection-diffusion coefficient and source term is considered in this paper. The existence and uniqueness of the solution has been proved. Further, a fitted finite difference method on Shishkin mesh is suggested to solve the problem. Numerical solution converges uniformly to the exact solution. The order of convergence of the numerical method presented here is of almost first order. Numerical results are provided to illustrate the theoretical results.