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A high-order numerical method for Caputo fractional Volterra integro-differential equations | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 16 آبان 1405 اصل مقاله (532.67 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.70992.3560 | ||
| نویسندگان | ||
| Aynalem Tafere Chekole1؛ Mesfin Woldaregay* 2؛ Kewani Welay Brhane1؛ Gemechis File Duressa3 | ||
| 1Department of Mathematics, Mekelle University, Mekelle, Ethiopia. | ||
| 2Department of Applied Mathematics, Adama Science and Technology University, Adama, Ethiopia. | ||
| 3Department of Mathematics, Jimma University, Jimma, Ethiopia. | ||
| چکیده | ||
| In this paper, we study fractional Volterra integro-differential equations with the Caputo derivative of order $\gamma \in (0,1)$. The domain is discretized using a uniform mesh. To approximate the solution, the fractional derivative is discretized using the L1-2-3 method, while Simpson's $\frac{1}{3}$ approximation is applied to approximate the Volterra integral term. The proposed method achieves third-order convergence for all $\gamma \in (0,1)$. The stability and convergence analysis are analyzed and realize that the approximate solution converges to the exact solution. The proposed method is compared with the results in the literature through examples supported by graphs and tables, and the results show that it achieves higher accuracy and order of convergence. | ||
| کلیدواژه‌ها | ||
| Fractional integro-differential equations؛ Caputo derivative؛ L1-2-3 scheme؛ Convergence analysis | ||
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آمار تعداد مشاهده مقاله: 4 تعداد دریافت فایل اصل مقاله: 4 |
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