Adapted Shifted ChebyshevU Operational Matrix of Derivatives: Two Algorithms for Solving Even-Order BVPs

Authors

Dina Abdelhamied, Department of Basic Science, Faculty of Engineering, May University in Cairo (MUC), Cairo, Egypt\\Helwan School of Numerical Analysis in Egypt (HSNAE), EgyptFollow
M. Abdelhakem, Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt\\ Basic Science Department, School of Engineering, Canadian International College, New Cairo, Egypt\\ Helwan School of Numerical Analysis in Egypt (HSNAE), EgyptFollow
M. El-Kady, Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt\\ Basic Science Department, School of Engineering, Canadian International College, New Cairo, Egypt\\ Helwan School of Numerical Analysis in Egypt (HSNAE), EgyptFollow
Y. H. Youssri, Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, EgyptFollow

Author Country (or Countries)

Egypt

Abstract

Herein, modified orthogonal polynomials are introduced. These polynomials are generated from the second kind of shifted Chebyshev polynomials on the interval [α, β]. The operational matrix of its derivative is constructed. The Tau and Galerkin method with the proposed orthogonal polynomials is used to solve the boundary value problems (BVPs) with even order. The effectiveness of these methods is proved through their application to several BVPs.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/170318

Recommended Citation

Abdelhamied, Dina; Abdelhakem, M.; El-Kady, M.; and H. Youssri, Y. (2023) "Adapted Shifted ChebyshevU Operational Matrix of Derivatives: Two Algorithms for Solving Even-Order BVPs," Applied Mathematics & Information Sciences: Vol. 17: Iss. 3, Article 18.
DOI: http://dx.doi.org/10.18576/amis/170318
Available at: https://digitalcommons.aaru.edu.jo/amis/vol17/iss3/18