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Article

Radical Petrov–Galerkin Approach for the Time-Fractional KdV–Burgers’ Equation

by
Youssri Hassan Youssri
1,2,* and
Ahmed Gamal Atta
3
1
Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
2
Faculty of Engineering, Egypt University of Informatics, New Administrative Capital 19519, Egypt
3
Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11341, Egypt
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2024, 29(6), 107; https://doi.org/10.3390/mca29060107
Submission received: 4 November 2024 / Revised: 15 November 2024 / Accepted: 19 November 2024 / Published: 21 November 2024
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Abstract

This paper presents a novel numerical spectral scheme to handle the time-fractional KdV–Burgers’ equation, which is very important in both physics and engineering. The scheme basically uses the tau approach combined with Gegenbauer polynomials to provide accurate and stable numerical solutions. Instead of solving the differential problem together with the conditions, we solve a system of algebraic equations. The method can handle complex boundary conditions. Some numerical experiments are exhibited to demonstrate that this approach is highly efficient and produces results that are better than some existing numerical methods in the literature. This technique offers more advanced solutions for time-fractional problems in various fields.
Keywords: Gegenbauer polynomials; Petrov–Galerkin method; time-fractional KdV–Burgers’ equation Gegenbauer polynomials; Petrov–Galerkin method; time-fractional KdV–Burgers’ equation

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MDPI and ACS Style

Youssri, Y.H.; Atta, A.G. Radical Petrov–Galerkin Approach for the Time-Fractional KdV–Burgers’ Equation. Math. Comput. Appl. 2024, 29, 107. https://doi.org/10.3390/mca29060107

AMA Style

Youssri YH, Atta AG. Radical Petrov–Galerkin Approach for the Time-Fractional KdV–Burgers’ Equation. Mathematical and Computational Applications. 2024; 29(6):107. https://doi.org/10.3390/mca29060107

Chicago/Turabian Style

Youssri, Youssri Hassan, and Ahmed Gamal Atta. 2024. "Radical Petrov–Galerkin Approach for the Time-Fractional KdV–Burgers’ Equation" Mathematical and Computational Applications 29, no. 6: 107. https://doi.org/10.3390/mca29060107

APA Style

Youssri, Y. H., & Atta, A. G. (2024). Radical Petrov–Galerkin Approach for the Time-Fractional KdV–Burgers’ Equation. Mathematical and Computational Applications, 29(6), 107. https://doi.org/10.3390/mca29060107

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