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An efficient algorithm for computing the eigenvalues of conformable Sturm-Liouville problem | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 29 آبان 1402 اصل مقاله (1.09 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2023.57436.2403 | ||
| نویسندگان | ||
| Hanif Mirzaei* 1؛ Mahmood Emami1؛ Kazem Ghanbari1؛ Mohammad Shahriari2 | ||
| 1Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran. | ||
| 2Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran. | ||
| چکیده | ||
| In this paper, Computing the eigenvalues of Conformable Sturm-Liouville Problem (CSLP) of order $2 \alpha$, $\frac{1}{2}<\alpha \leq 1$, and dirichlet boundary conditions is considered. For this aim, CSLP is discretized to obtain a matrix eigenvalue problem (MEP) using finite element method with fractional shape functions. Then by a method based on asymptotic form of the eigenvalues we correct the eigenvalues of MEP to obtain efficient approximations for the eigenvalues of CSLP. Finally, some numerical examples to show the efficiency of the proposed method are given. Numerical results show that for the $n$th eigenvalue the correction technique reduces the error order from $O(n^4h^2)$ to $O(n^2h^2)$. | ||
| کلیدواژه‌ها | ||
| Sturm-Liouville problem؛ Conformable derivative؛ Finite element method؛ Correction idea | ||
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آمار تعداد مشاهده مقاله: 62 تعداد دریافت فایل اصل مقاله: 88 |
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