Spectral Collocation Algorithm for the Fractional Bratu Equation via Hexic Shifted Chebyshev Polynomials

Atta, Ahmed Gamal; Soliman, Jomana Farag; Elsaeed, Elaf Wael; Elsaeed, Mostafa Wael; Youssri, Youssri Hassan

doi:10.22034/cmde.2024.61045.2621

Spectral Collocation Algorithm for the Fractional Bratu Equation via Hexic Shifted Chebyshev Polynomials

Document Type : Research Paper

Authors

¹ Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11341, Egypt.

² Department of Mathematics, Faculty of Science, Galala University, Egypt.

³ Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt.

10.22034/cmde.2024.61045.2621

Abstract

This paper offers a numerical collocation scheme for solving the fractional nonlinear Bratu differential equation. We obtain a system of nonlinear equations using our spectral collocation method, which we then solve iteratively using Newton's method to obtain an approximate solution. Additionally, numerical comparisons are made between the proposed strategy and several numerical strategies documented in various literatures. The numerical findings verify the accuracy, computational efficiency, and ease of use of the recommended approach.

Keywords

Main Subjects