Hybrid Fitted Numerical Scheme for Singularly Perturbed Spatiotemporal Delay Differential Equations

Abstract

In this study, a hybrid scheme is presented to solve a singularly perturbed time‐delay differential equation with a delay and advance term in the spatial variable. The scheme combines the midpoint upwind scheme and the cubic spline difference scheme in the outer and inner layer regions, respectively, on a nonuniform mesh for the spatial discretization, and the Crank–Nicolson method on a uniform mesh for the time derivative discretization is applied. The suggested approach’s stability and error analysis have been performed. The theoretical results are verified through numerical experiments; the computational result shows that the proposed method is almost second‐order uniformly convergent with a logarithmic factor, which is in the right agreement with the theoretical result. Furthermore, a comparison is carried out, and the results of the suggested scheme give better results as compared to the study available in the literature.