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Higher order multi-step methods for fractional differential equations | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 10 مرداد 1405 اصل مقاله (1.23 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.70049.3462 | ||
| نویسندگان | ||
| Mahmoud Ghassemzadeh1؛ Ali Shokri* 2؛ Mohammad Mehdizadeh Khalsaraei1؛ Mir Kamal Mirnia3 | ||
| 1Department of Mathematics, Faculty of Basic Science, University of Maragheh, Maragheh, Iran. | ||
| 2Department of Applied Mathematics, Sahand University of Technology, Sahand New-Town, Tabriz, Iran. | ||
| 3Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, University of Tabriz, Tabriz, Iran. | ||
| چکیده | ||
| This paper introduces NewFLMM, a novel family of high-order fractional linear multistep methods specifically designed to solve Caputo fractional differential equations. By integrating higher-order derivatives of the vector field, the proposed schemes significantly extend the stability regions beyond the inherent limits of classical fractional backward differentiation formulae (FBDF). We develop efficient recursive algorithms for coefficient generation and provide a rigorous stability analysis for orders k = 2, 3, and 4. The theoretical framework establishes both zero-stability and convergence properties. Numerical experiments on stiff and nonlinear systems confirm that NewFLMM provides superior accuracy and substantially broader stability domains than conventional methods. To facilitate implementation, comprehensive coefficient tables are provided. | ||
| کلیدواژهها | ||
| Fractional Methods؛ Stability Region؛ Numerical Methods؛ Convergence Order | ||
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آمار تعداد مشاهده مقاله: 5 تعداد دریافت فایل اصل مقاله: 3 |
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