Hybrid Fitted Numerical Scheme for Singularly Perturbed Spatiotemporal Delay Differential Equations

Mulunesh Amsalu Ayele and Dagnachew Mengstie Tefera

International Journal of Differential Equations, 2026, vol. 2026, 1-17

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.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:7175436

DOI: 10.1155/ijde/7175436

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