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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2025 Volume 65, Number 2, Pages 252–269 (Mi zvmmf11927)

Papers published in the English version of the journal

Fitted operator methods for singularly perturbed differential-difference equations via splines

K. Vivek, R. Nageshwar Rao

Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, 632014, Vellore, Tamil Nadu, India

Abstract: Spline in compression and adaptive spline approaches are used to solve a singularly perturbed differential-difference equation with delay and advanced terms. A fitting factor is used for resolving the boundary layer. Theoretical rate of convergence is calculated and supported by the numerical results for test problems. The layer behavior for various values of the perturbation parameter and the shift parameters is depicted in graphs.

Key words: singular perturbation problems, differential-difference equations, numerical methods, adaptive spline, spline in compression.

Received: 26.07.2024
Revised: 24.10.2024
Accepted: 26.03.2025

Language: English


 English version:
Computational Mathematics and Mathematical Physics, 2025, 65:2, 252–269


© Steklov Math. Inst. of RAS, 2025