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A Spectral Tau Method Based on Lucas Polynomial Approximation for Solving the Nonlinear Fractional Riccati Equation | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 22 شهریور 1404 اصل مقاله (1.4 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.67681.3237 | ||
| نویسندگان | ||
| Youssri Hassan Youssri* 1؛ Ahmed Gamal Atta2 | ||
| 1Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt. | ||
| 2Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11341, Egypt. | ||
| چکیده | ||
| The nonlinear fractional Riccati equation (NFRE) can be solved using a unique spectral tau approach in this study that uses Lucas polynomials as basis functions. The fractional Caputo derivative and nonlinear terms can be handled effectively by explicit operational formulations when the Lucas basis is used. A tau projection is used to convert the problem into a nonlinear algebraic system, which is then solved by Gaussian elimination. The correctness and quick convergence of the suggested method are shown by a number of numerical tests that are backed by error analysis. | ||
| کلیدواژه‌ها | ||
| Lucas polynomials؛ Spectral methods؛ Nonlinear fractional Riccati equation؛ Convergence analysis | ||
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آمار تعداد مشاهده مقاله: 2 |
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