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Numerical Solution of Variable-Order Fractional Bagley-Torvik Equation Using Multi-Domain Legendre Collocation Approach | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 11 دی 1404 اصل مقاله (1.22 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.70146.3472 | ||
| نویسندگان | ||
| Negisa Ayazi1؛ Payam Mokhtary* 2 | ||
| 1Department of Mathematics, Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran. | ||
| 2Department of Mathematics, Faculty of Sciences, Sahand University of Technology, Tabriz, Iran. | ||
| چکیده | ||
| This paper introduces a novel multi-domain Legendre-collocation method for the numerical solution of the variable-order fractional Bagley-Torvik equation. To address the computational challenges posed by variable-order fractional derivatives and their weakly singular kernels, an operational matrix formulation is developed, providing a highly efficient alternative to classical three-term recurrence schemes based on Legendre polynomials. The domain decomposition strategy enables local evaluation of the memory integral within each subdomain, thereby preserving spectral accuracy while mitigating the stability degradation and round-off error accumulation often encountered in global spectral methods over extended intervals. Numerical experiments confirm the proposed method's spectral convergence, stability, and computational efficiency. The results highlight the method's potential as a reliable and accurate framework for solving a broad class of variable-order fractional differential equations. | ||
| کلیدواژهها | ||
| Variable-order fractional Bagley-Torvik equation؛ Multi-domain Legendre-collocation method؛ Domain decomposition | ||
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آمار تعداد مشاهده مقاله: 75 تعداد دریافت فایل اصل مقاله: 122 |
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