Hybrid Shifted Gegenbauer Integral–Pseudospectral Method for Solving Time-Fractional Benjamin–Bona–Mahony–Burgers Equation
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| הוצא לאור ב: | Mathematics vol. 13, no. 16 (2025), p. 2678-2698 |
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MDPI AG
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| גישה מקוונת: | Citation/Abstract Full Text + Graphics Full Text - PDF |
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| 045 | 2 | |b d20250101 |b d20251231 | |
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| 100 | 1 | |a Elgindy, Kareem T |u Department of Mathematics and Sciences, College of Humanities and Sciences, Ajman University, Ajman P.O. Box 346, United Arab Emirates; k.elgindy@ajman.ac.ae | |
| 245 | 1 | |a Hybrid Shifted Gegenbauer Integral–Pseudospectral Method for Solving Time-Fractional Benjamin–Bona–Mahony–Burgers Equation | |
| 260 | |b MDPI AG |c 2025 | ||
| 513 | |a Journal Article | ||
| 520 | 3 | |a This paper introduces a novel hybrid shifted Gegenbauer integral–pseudospectral (HSG-IPS) method to solve the time-fractional Benjamin–Bona–Mahony–Burgers (FBBMB) equation with high accuracy. The approach transforms the equation into a form with only a first-order derivative, which is approximated using a stable shifted Gegenbauer differentiation matrix (SGDM), while other terms are computed with precise quadrature rules. By integrating advanced techniques such as the shifted Gegenbauer pseudospectral method (SGPS), fractional derivative and integral approximations, and barycentric integration matrices, the HSG-IPS method achieves spectral accuracy. Numerical results show it reduces average absolute errors (AAEs) by up to 99.99% compared to methods like Crank–Nicolson linearized difference scheme (CNLDS) and finite integration method using Chebyshev polynomial (FIM-CBS), with computational times as low as 0.04–0.05 s. The method’s stability is improved by avoiding ill-conditioned high-order derivative approximations, and its efficiency is boosted by precomputed matrices and Kronecker product structures. Robust across various fractional orders, the HSG-IPS method offers a powerful tool for modeling wave propagation and nonlinear phenomena in fractional calculus applications. | |
| 653 | |a Accuracy | ||
| 653 | |a Propagation | ||
| 653 | |a Calculus | ||
| 653 | |a Viscosity | ||
| 653 | |a Quadratures | ||
| 653 | |a Polynomials | ||
| 653 | |a Chebyshev approximation | ||
| 653 | |a Approximation | ||
| 653 | |a Numerical analysis | ||
| 653 | |a Wave propagation | ||
| 653 | |a Methods | ||
| 653 | |a Error reduction | ||
| 653 | |a Fractional calculus | ||
| 653 | |a Dengue fever | ||
| 653 | |a Viscoelasticity | ||
| 653 | |a Burgers equation | ||
| 653 | |a Nonlinear phenomena | ||
| 653 | |a Derivatives | ||
| 653 | |a Efficiency | ||
| 653 | |a Integrals | ||
| 653 | |a Spectral methods | ||
| 773 | 0 | |t Mathematics |g vol. 13, no. 16 (2025), p. 2678-2698 | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3244045287/abstract/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text + Graphics |u https://www.proquest.com/docview/3244045287/fulltextwithgraphics/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3244045287/fulltextPDF/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |