Second kind Chebyshev polynomial differentiation and integration matrices for solving some mathematical models
Mahmoud, S., El-Kady, M., Abdelhakem, M. (2025). Second kind Chebyshev polynomial differentiation and integration matrices for solving some mathematical models. EKB Journal Management System, 5(1), 1-10. doi: 10.21608/abas.2025.403302.1066
Somaya Mahmoud; Mamdouh El-Kady; Mohamed A Abdelhakem. "Second kind Chebyshev polynomial differentiation and integration matrices for solving some mathematical models". EKB Journal Management System, 5, 1, 2025, 1-10. doi: 10.21608/abas.2025.403302.1066
Mahmoud, S., El-Kady, M., Abdelhakem, M. (2025). 'Second kind Chebyshev polynomial differentiation and integration matrices for solving some mathematical models', EKB Journal Management System, 5(1), pp. 1-10. doi: 10.21608/abas.2025.403302.1066
Mahmoud, S., El-Kady, M., Abdelhakem, M. Second kind Chebyshev polynomial differentiation and integration matrices for solving some mathematical models. EKB Journal Management System, 2025; 5(1): 1-10. doi: 10.21608/abas.2025.403302.1066

Second kind Chebyshev polynomial differentiation and integration matrices for solving some mathematical models

Advances in Basic and Applied Sciences
Volume 5, Issue 1, August 2025, Page 1-10  XML PDF (773.16 K)
Document Type: Original Article
DOI: 10.21608/abas.2025.403302.1066
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Authors
Somaya Mahmoudorcid 1; Mamdouh El-Kadyorcid 2; Mohamed A Abdelhakem email orcid 3
1Basic Science Department, Modern Academy for Computer Science and Management Technology, Cairo, Egypt
2Mathematics Department, Faculty of Science, Helwan University Ain Helwan, Cairo, Egypt
3Mathematics Department, Faculty of Science, Helwan University, Ain Helwan, Cairo, Egypt,
Abstract
In the current work, new pseud-spectral differentiation and integration matrices have been constructed via the second kind of Chebyshev polynomials as a basis function. To achieve that purpose, the continuous inner product of the spectral expansion summation is transformed into a discrete one via the Trapezoidal integration technique. Hence, the given problem, differential, integral, or integro-differential equations, is transformed into a system of algebraic equations. Unlike the standard spectral methods, the algebraic system of equations’ unknowns are the dependent variables’ values at equidistant points. The constructed pseud-spectral differentiation and integration matrices have been tested to approximate the differentiation and integration of known functions to examine their applicability as differentiation and integration operators. In addition, the matrices have been used to approximate the solution of differential, integral equations, and integro-differential equations. Some of the presented differential, integral, and integro-differential equations represent models concerning real-life applications. Log error figures have shown the stability of the results.
Keywords
Second Kind of Chebyshev Polynomials; Pseudo-spectral Method; Differentiation and Integration Matrices; Ordinary Differential Equation; Integro-Differential Equation; Real-life Applications
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