An efficient algorithm for computing the eigenvalues of conformable Sturm-Liouville problem

Mirzaei, Hanif; Emami, Mahmood; Ghanbari, Kazem; Shahriari, Mohammad

doi:10.22034/cmde.2023.57436.2403

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	An efficient algorithm for computing the eigenvalues of conformable Sturm-Liouville problem
Computational Methods for Differential Equations
مقاله 4، دوره 12، شماره 3، مهر 2024، صفحه 471-483 اصل مقاله (547.88 K)
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 the 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 the 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 elements method؛ Correction idea

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An efficient algorithm for computing the eigenvalues of conformable Sturm-Liouville problem