Fitted Numerical Method with Linear Interpolation for Third-Order Singularly Perturbed Delay Problems

Abstract

Singularly perturbed third-order ordinary delay differential equation with a discontinuous source term and discontinuous convection coefficient is considered in this article. To obtain a numerical approximate solution, a layer adapted mesh called the Shishkin mesh is constructed. On this mesh, a fitted finite difference method with piecewise linear interpolation is applied. Also, we present some classes of nonlinear problems. An error estimate is derived and is found to be of almost first-order convergence. Numerical results are given to validate the theoretical results