"Numerical Treatment of Special Types of Odd-Order Boundary Value Probl" by Waleed Mohamed Abd-Elhameed, Eid Hassan Doha et al.

Progress in Fractional Differentiation & Applications

Article Title

Numerical Treatment of Special Types of Odd-Order Boundary Value Problems Using Nonsymmetric Cases of Jacobi Polynomials

Authors

Waleed Mohamed Abd-Elhameed, Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt\\ Department of Mathematics, College of Science, University of Jeddah, Jeddah 23218, Saudi ArabiaFollow
Eid Hassan Doha, Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, EgyptFollow
Muhammad Mahmoud Alsuyuti, Department of Basic Science, Egyptian Academy for Engineering and Advanced Technology Affiliated to Ministry of Military Production, Cairo, EgyptFollow

Author Country (or Countries)

Egypt

Abstract

In this article, two new dual Petrov-Galerkin algorithms for solving high odd-order boundary value problems (BVPs) are presented and implemented. The philosophy of applying the Petrov-Galerkin method is built on choosing the trial and test functions such that they satisfy the underlying boundary and dual boundary conditions, respectively. The presented approaches are based on employing the shifted Chebyshev polynomials of third and fourth kinds, respectively, as basis functions. Several numerical experiments are included to ascertain the validity and efficiency of the proposed algorithms. Moreover, comparisons with some other numerical methods in the literature are given.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/pfda/080210

Recommended Citation

Mohamed Abd-Elhameed, Waleed; Hassan Doha, Eid; and Mahmoud Alsuyuti, Muhammad (2022) "Numerical Treatment of Special Types of Odd-Order Boundary Value Problems Using Nonsymmetric Cases of Jacobi Polynomials," Progress in Fractional Differentiation & Applications: Vol. 8: Iss. 2, Article 10.
DOI: http://dx.doi.org/10.18576/pfda/080210
Available at: https://digitalcommons.aaru.edu.jo/pfda/vol8/iss2/10

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