Treatment of Singularly Perturbed Differential Equations with Delay and Shift Using Haar Wavelet Collocation Method

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Published: Nov 1, 2022
DOI: https://doi.org/10.5556/j.tkjm.53.2022.3250
Keywords:
Haar wavelet Collocation grid Singular perturbation Delay Shift

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Akmal Raza
Jamia Millia Islamia
https://orcid.org/0000-0002-6135-2822
Arshad Khan
Department of Mathematics, Jamia Millia Islamia, New Delhi-110025, India

Abstract

An efficient Haar wavelet collocation method is proposed for the numerical solution of singularly perturbed differential equations with delay and shift. Taylor series (upto the first order) is used to convert the problem with delay and shift into a new problem without the delay and shift and then  solved by Haar wavelet collocation method, which reduces the time and complexity of the system. Further, we apply the Haar wavelet collocation method directly  to solve the problems. Also, we demonstrated several test examples to show the accuracy and efficiency of the Haar wavelet collocation method and compared our results with the finite difference and fitted operator finite difference method [11], [28].

Article Details

How to Cite
Raza, A., & Khan, A. (2022). Treatment of Singularly Perturbed Differential Equations with Delay and Shift Using Haar Wavelet Collocation Method. Tamkang Journal of Mathematics, 53(4), 303–322. https://doi.org/10.5556/j.tkjm.53.2022.3250
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.

Author Biography

Akmal Raza, Jamia Millia Islamia

Research Scholar 

Department of Mathematics Jamia MIllia Islamia

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