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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Marwa Gamal & M. El-Kady & M. Abdelhakem, 2024. "Solving real-life BVPs via the second derivative Chebyshev pseudo-Galerkin method," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 35(07), pages 1-20, July.
    • Handle: RePEc:wsi:ijmpcx:v:35:y:2024:i:07:n:s012918312450089x
    DOI: 10.1142/S012918312450089X
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