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Numerical Analysis of a Nonlinear Fractional Cable Model Using the Galerkin Spectral Element Method | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 16 مرداد 1405 اصل مقاله (1.47 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.71304.3583 | ||
| نویسندگان | ||
| Hamideh Taji؛ Mojtaba Fardi* ؛ Mehdi Ghasemi | ||
| Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, Shahrekord 88186-34141, Iran. | ||
| چکیده | ||
| In this paper, we propose an efficient numerical method for solving the nonlinear fractional cable model, which includes multi-term time-fractional derivatives in the Riemann–Liouville sense. The model describes memory effects and anomalous diffusion through distinct fractional orders in both the diffusion and reaction terms. To discretize the problem, we employ a high-order finite difference scheme in time and a Legendre Galerkin spectral element method in space. We prove the stability and convergence of the time-discrete scheme and provide an error estimate for the fully discrete scheme. Numerical experiments are conducted to rigorously investigate the accuracy and efficiency of the proposed approach, demonstrating its effectiveness across various parameter settings. | ||
| کلیدواژهها | ||
| Nonlinear Fractional Cable Model؛ Galerkin Spectral Element Method؛ Legendre Polynomials | ||
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آمار تعداد مشاهده مقاله: 42 تعداد دریافت فایل اصل مقاله: 31 |
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