Version 1
: Received: 18 October 2023 / Approved: 19 October 2023 / Online: 19 October 2023 (10:03:16 CEST)
How to cite:
Ejere, A. H. Parameter-Robust Numerical Scheme for Computing Singularly Perturbed Differential Equations with Mixed Large Shifts. Preprints2023, 2023101241. https://doi.org/10.20944/preprints202310.1241.v1
Ejere, A. H. Parameter-Robust Numerical Scheme for Computing Singularly Perturbed Differential Equations with Mixed Large Shifts. Preprints 2023, 2023101241. https://doi.org/10.20944/preprints202310.1241.v1
Ejere, A. H. Parameter-Robust Numerical Scheme for Computing Singularly Perturbed Differential Equations with Mixed Large Shifts. Preprints2023, 2023101241. https://doi.org/10.20944/preprints202310.1241.v1
APA Style
Ejere, A. H. (2023). Parameter-Robust Numerical Scheme for Computing Singularly Perturbed Differential Equations with Mixed Large Shifts. Preprints. https://doi.org/10.20944/preprints202310.1241.v1
Chicago/Turabian Style
Ejere, A. H. 2023 "Parameter-Robust Numerical Scheme for Computing Singularly Perturbed Differential Equations with Mixed Large Shifts" Preprints. https://doi.org/10.20944/preprints202310.1241.v1
Abstract
This study focuses on the formulation and analysis of a numerical method to compute singularly perturbed functional differential equations (SP-FDEs) involving large mixed shifts. SP-FDEs are a class of differential equations with both shifts and small perturbation parameter. Such equations arise in various scientific fields to model phenomena with memory effects and perturbed dynamics. In this particular study, the considered SP-FDEs involve large negative shift (delay) and large positive shift (advance). Dealing with large mixed shifts in SP-FDEs gives rise to challenges in terms of stability analysis, numerical methods, and convergence of a solution. In this paper, the influence of the large mixed shifts is treated by choosing a uniform mesh discretized in such a way that the term with the shifts lie on the nodal points. Then, using the Numerov’s finite difference method, the continuous problem is transformed into a finite difference scheme and the influence of the perturbation parameter is handled by introducing a fitting factor in the difference scheme. Stability estimate and convergence analysis of the developed scheme are investigated and proved. Numerical experiments are carried out to demonstrate the validity and applicability of the developed scheme. It is shown that the numerical scheme obtained in this work is parameter-robust of second order convergence rate.
Computer Science and Mathematics, Computational Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
