Solving real-life BVPs via the second derivative Chebyshev pseudo-Galerkin method

Marwa Gamal, M. El-Kady and M. Abdelhakem
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Marwa Gamal: Department of Basic Science, Faculty of Engineering, May University in Cairo (MUC), Cairo, Egypt§Helwan School of Numerical Analysis in Egypt (HSNAE), Egypt
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), Egypt
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), Egypt

International Journal of Modern Physics C (IJMPC), 2024, vol. 35, issue 07, 1-20

Abstract: The aim of this paper is to use the second derivative of Chebyshev polynomials (SDCHPs) as basis functions for solving linear and nonlinear boundary value problems (BVPs). Then, the operational matrix for the derivative was established by using SDCHPs. The established matrix via mixing between two spectral methods, collocation and Galerkin, has been applied to solve BVPs. Consequently, an error analysis is investigated to ensure the convergence of the technique used. Finally, we solved some problems involving real-life applications and compared their solutions with exact and other solutions from different methods to verify the accuracy and efficiency of this method.

Keywords: Second derivative of Chebyshev polynomials; spectral method; pseudo-Galerkin; error analysis; Lane–Emden; fluid (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S012918312450089X

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