An exponentially fitted scheme for solving singularly perturbed delay problems

This paper presents a new exponentially fitted three point scheme for solving singularly perturbed delay problems with boundary layer at left (or right) end of the domain. Scheme is derived using the exact and approximate rule of integration with finite difference approximations of first derivative. A fitting factor is introduced in the scheme using the concept of singular perturbation. Thomas algorithm is used to solve the resulting tri-diagonal system. Convergence analysis of the proposed method is given. Applicability of the method is shown by implementing it on several linear and nonlinear example problems with the various values of the delay parameter δ and the perturbation parameter ε. Numerical results in terms of maximum absolute errors are presented to illustrate the efficiency of the method. It is observed that the method is able to approximates the solution very well