Objectives: An accurate exponential fitted numerical method is developed to solve singularly perturbed time lag problem. Solution of the problem exhibits a boundary layer as the perturbation parameter approach to zero. A priori bounds and properties on the continuous solution is discussed.
Result: The backward-Euler method is applied in time direction and higher order finite difference method is employed to the spatial derivative approximation. An exponential fitting factor is induced on the difference scheme for stabilizing the computed solution. Using comparison principle, stability of the method is examined and analyzed. It is proved that the method converges uniformly with linear order of convergence both in space and time. To validate theoretical findings of the scheme, two test examples are given. Comparison is employed with the result available in the literature and it indicates that the proposed method has better accuracy than the schemes in literature.