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Ritz-Optimization Approach for Solving Various Fractional Problems | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 08 اردیبهشت 1405 اصل مقاله (1.43 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.67442.3212 | ||
| نویسندگان | ||
| Haniye Dehestani؛ Yadollah Ordokhani* | ||
| Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran. | ||
| چکیده | ||
| This work presents a composite approach for solving three types of problems by integrating multiple numerical methods. The proposed method incorporates the optimization technique, the Ritz method, the Legendre-Gauss quadrature rule, and fractional Mott functions (FMFs) as basis functions. Additionally, the derivative matrices of FMFs are utilized in the numerical algorithm. The core idea of our approach begins with applying the Ritz method while considering the given conditions. Next, using the Legendre-Gauss quadrature rule and the optimization method, we approximate all functions involved in the problem. Specifically, the hidden layer of the optimization framework is constructed using FMFs and their corresponding derivative matrices. Finally, through the classical optimization method, the problem is transformed into a system of algebraic equations. Furthermore, we conduct an error analysis of the integrals that appear in the problems. To demonstrate the effectiveness and applicability of the proposed scheme, we solve different problems. | ||
| کلیدواژهها | ||
| Ritz method؛ Optimization method؛ Fractional Mott functions؛ Variable-order fractional derivative؛ Legendre-Gauss quadrature rule | ||
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