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Operational discrete Petrov-Galerkin method for solving distributed order FDEs | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 26 اردیبهشت 1405 اصل مقاله (1.15 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.71162.3579 | ||
| نویسندگان | ||
| Zeynab Saki؛ Payam Mokhtary* | ||
| Department of Mathematics, Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran. | ||
| چکیده | ||
| This study presents a novel discrete Petrov-Galerkin method for solving distributed-order fractional differential equations, where fractional derivatives are expressed in the Caputo sense. The proposed approach begins by reducing the distributed-order equation to a multi-term fractional equation using the Newton-Cotes quadrature rule, thereby simplifying the numerical approximation process. The discrete Petrov-Galerkin framework utilizes generalized Jacobi polynomials as basis functions and fractional Legendre functions as test functions, chosen for their robust approximation capabilities. By exploiting these mathematical properties, the method transforms the problem into a system of algebraic equations. A comprehensive convergence analysis is conducted to validate the accuracy and reliability of the method. The effectiveness of the proposed approach is further illustrated through three numerical examples, demonstrating its superior performance compared to existing techniques in terms of accuracy and computational efficiency. | ||
| کلیدواژهها | ||
| Distributed-order fractional differential equation (DOFDE)؛ Discrete Petrov-Galerkin method؛ fractional Legendre functions | ||
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آمار تعداد مشاهده مقاله: 66 تعداد دریافت فایل اصل مقاله: 52 |
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