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

Mohamed Nasseh Nadir; Adel Jawahdou

doi:10.35819/remat2024v10i1id6699

Autores/as

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

Palabras clave:

polinomios de Chebyshev, ecuaciones integrales de Volterra-Fredholm, problemas mal planteados, ecuaciones perturbadas

Resumen

Se han estudiado y discutido muchos métodos para resolver la ecuación integral de Volterra mal puesta y la ecuación integral de Fredholm mal puesta, pero no ambas. En este trabajo resolvemos numéricamente la ecuación integral mal puesta de Volterra-Fredholm del primer tipo, reemplazada por su ecuación perturbada. Resolvemos esta última usando polinomios de Chebyshev del primer tipo y, en esta resolución, creemos que el método técnico de esta resolución es mejor, más sencillo y menos complicado que la regularización de Tikhonov. Esta simplicidad se verifica a través de algunos ejemplos.

Descargas

Los datos de descarga aún no están disponibles.

Biografía del autor/a

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

Referencias

HADAMARD, J. Lectures on Cauchy's problem in linear partial differential equations. New Haven: Yale University Press, 1923. Available in: https://archive.org/details/lecturesoncauchy00hadauoft. Access at: February 5, 2024.

KUMAR, J.; MANCHANDA, P.; POOJA. Numerical solution of Fredholm integral equations of the first kind using Legendre wavelets collocation method. International Journal of Pure and Applied Mathematics. v. 117, n. 1, p. 33-43, 2017. DOI: https://doi.org/10.12732/ijpam.v117i1.4.

LAKHAL, A.; NADIR, M.; NADIR, M. N. Application of Chebyshev polynomials to Volterra-Fredholm integral equations. Australian Journal of Mathematical Analysis and Applications. v. 19, n. 2, p. 1-8, 2022. Available in: https://ajmaa.org/searchroot/files/pdf/v19n2/v19i2p8.pdf. Access at: February 5, 2024.

LAMM, P. K. A Survey of Regularization Methods for First-Kind Volterra Equations. Vienna, New York: Springer, 2000, p. 53-82. Available in: https://users.math.msu.edu/users/lamm/Preprints/Mt_Holyoke_Survey/index.html. Access at: February 5, 2024.

MALEKNEJAD, K.; KAJANI, M. T.; MAHMOUDI, Y. Numerical solution of linear Fredholm and Volterra integral equations of the second kind using Legendre wavelets. Journal of Sciences, Islamic Republic of Iran. v. 13, n. 2, p. 161-166, 2002. Available in: https://journal.ut.ac.ir/article_31744_3af2254cc9e8b974559cf3ec796e9692.pdf. Access at: February 5, 2024.

NADIR, M.; BENDJABRI, N. On the invertibility of the Cauchy singular integral. International Journal of Mathematics and Computation. v. 29, n. 2, p. 113-118, 2018. Available in: http://www.ceser.in/ceserp/index.php/ijmc/article/view/5496. Access at: February 5, 2024.

NADIR, M.; DJAIDJA, N. Approximation method for Volterra integral equation of the first kind. International Journal of Mathematics and Computation. v. 29, n. 4, p. 67-72, 2018. Available in: http://www.ceser.in/ceserp/index.php/ijmc/article/view/5677. Access at: February 5, 2024.

NADIR, M.; DJAIDJA, N. Comparison between Taylor and perturbed method for Volterra integral equation of the first kind. Numerical Algebra, Control and Optimization. v. 11, n. 4, p. 487-493, 2021. DOI: https://doi.org/10.3934/naco.2020039.