Fitted Numerical Scheme for Solving Singularly Perturbed Parabolic Delay Partial Differential Equations

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Published: Nov 1, 2022
DOI: https://doi.org/10.5556/j.tkjm.53.2022.3638
Keywords:
Delay differential equations, Exponentially fi tted scheme, Uniform convergence

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Gemechis File Duressa
Department of Mathematics, Jimma University, Ethiopia
https://orcid.org/0000-0003-1889-4690
Mesfin Mekuria Woldaregay
Department of Mathematics, Jimma University
https://orcid.org/0000-0002-6555-7534

Abstract




In this paper, exponentially fitted finite difference scheme is developed for solving singularly perturbed parabolic delay partial differential equations having small delay on the spatial variable. The term with the delay is approximated using Taylor series approximation. The resulting singularly perturbed parabolic partial differential equation is treated using im- plicit Euler method in the temporal discretization with exponentially fitted operator finite difference method in the spatial discretization. The parameter uniform convergence analysis has been carried out with the order of convergence one. Test examples and numerical results are considered to validate the theoretical analysis of the scheme.




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How to Cite
Duressa, G. F., & Woldaregay, M. M. (2022). Fitted Numerical Scheme for Solving Singularly Perturbed Parabolic Delay Partial Differential Equations. Tamkang Journal of Mathematics, 53(4), 345–362. https://doi.org/10.5556/j.tkjm.53.2022.3638
Issue
Vol. 53 No. 4 (2022)
Section
Papers
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This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

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