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

سال انتشار: 1403
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 89

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شناسه ملی سند علمی:

JR_CMDE-12-3_004

تاریخ نمایه سازی: 23 خرداد 1403

چکیده مقاله:

In this paper, Computing the eigenvalues of the Conformable Sturm-Liouville Problem (CSLP) of order ۲ \alpha, \frac{۱}{۲}<\alpha \leq ۱, 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 nth eigenvalue, the correction technique reduces the error order from O(n^۴h^۲) to O(n^۲h^۲).

نویسندگان

Hanif Mirzaei

Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran.

Mahmood Emami

Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran.

Kazem Ghanbari

Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran.

Mohammad Shahriari

Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran.