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Implicit numerical approach for nonlinear fractional differential equations with a time non-sigular kernel and mixed boundary conditions | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 25 دی 1404 اصل مقاله (1.68 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.62977.2807 | ||
| نویسندگان | ||
| Leyla Azami؛ Amir Hossein Refahi Sheikhani* ؛ Hashem Saberi Najafi | ||
| Department of Applied Mathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran. | ||
| چکیده | ||
| This study focuses on the numerical solution of the time-fractional nonlinear Cable equation with the Caputo–Fabrizio derivative using an implicit Crank–Nicolson scheme. To demonstrate the versatility and robustness of the proposed method, we investigate the problem under both Dirichlet and Neumann boundary condition. The Stability analysis confirms that the scheme is unconditionally stable. To further evaluate the robustness of the difference scheme, the same numerical framework is applied to the fractional Burgers equation under identical settings. Numerical experiments are conducted to verify the stability and accuracy of the method, and to illustrate its applicability in simulating both signal propagation in nerve fibers (cable equation) and viscous transport (Burgers equation). | ||
| کلیدواژهها | ||
| Cranck-Nicholson scheme؛ nonlinear Cable equation؛ Stability؛ Dirichlet conditions؛ Neumann boundary conditions | ||
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آمار تعداد مشاهده مقاله: 25 تعداد دریافت فایل اصل مقاله: 30 |
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