Efficient Spectral Galerkin and Collocation Approaches Using Telephone Polynomials for Solving Some Models of Differential Equations with Convergence Analysis

Ramy Mahmoud Hafez, Hany Mostafa Ahmed, Omar Mazen Alqubori, Amr Kamel Amin and Waleed Mohamed Abd-Elhameed ()
Additional contact information
Ramy Mahmoud Hafez: Department of Mathematics, Faculty of Education, Matrouh University, Cairo 51511, Egypt
Hany Mostafa Ahmed: Department of Mathematics, Faculty of Technology and Education, Helwan University, Cairo 11281, Egypt
Omar Mazen Alqubori: Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 23831, Saudi Arabia
Amr Kamel Amin: Department of Mathematics, Adham University College, Umm Al-Qura University, Makkah 28653, Saudi Arabia
Waleed Mohamed Abd-Elhameed: Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt

Mathematics, 2025, vol. 13, issue 6, 1-29

Abstract: This study presents Galerkin and collocation algorithms based on Telephone polynomials (TelPs) for effectively solving high-order linear and non-linear ordinary differential equations (ODEs) and ODE systems, including those with homogeneous and nonhomogeneous initial conditions (ICs). The suggested approach also handles partial differential equations (PDEs), emphasizing hyperbolic PDEs. The primary contribution is to use suitable combinations of the TelPs, which significantly streamlines the numerical implementation. A comprehensive study has been conducted on the convergence of the utilized telephone expansions. Compared to the current spectral approaches, the proposed algorithms exhibit greater accuracy and convergence, as demonstrated by several illustrative examples that prove their applicability and efficiency.

Keywords: telephone numbers; telephone polynomials; spectral methods; partial differential equations; convergence analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/6/918/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/6/918/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:6:p:918-:d:1609264

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().