Chebyshev polynomials to Volterra-Fredholm integral equations of the first kind

Mohamed Nasseh Nadir; Adel Jawahdou

doi:10.35819/remat2024v10i1id6699

Authors

Mohamed Nasseh Nadir University of Carthage, Faculty of Sciences of Bizerte, Department of Mathematics, Jarzouna, Tunisia https://orcid.org/0009-0007-1593-8113
Adel Jawahdou University of Carthage, Institute of Engineering of Bizerte, Department of Mathematics, Jarzouna, Tunisia https://orcid.org/0000-0002-3551-1236

DOI:

https://doi.org/10.35819/remat2024v10i1id6699

Keywords:

Chebyshev polynomials, Volterra-Fredholm integral equations, ill-posed problems, perturbed equations

Abstract

Numerous methods have been studied and discussed for solving ill-posed Volterra integral equations and ill-posed Fredholm integral equations, but rarely for both simultaneously. In this study, we focus on numerically solving the ill-posed Volterra-Fredholm integral equation of the first kind by replacing it with its perturbed counterpart. We employ Chebyshev polynomials of the first kind to solve the perturbed equation. Our findings suggest that this technical approach is superior to the regularization method of Tikhonov. It is simpler, less cumbersome, and this simplicity is demonstrated through various examples.

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Author Biographies

Mohamed Nasseh Nadir, University of Carthage, Faculty of Sciences of Bizerte, Department of Mathematics, Jarzouna, Tunisia

https://orcid.org/0009-0007-1593-8113
Adel Jawahdou, University of Carthage, Institute of Engineering of Bizerte, Department of Mathematics, Jarzouna, Tunisia

https://orcid.org/0000-0002-3551-1236

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