An efficient algorithm for computing the eigenvalues of conformable Sturm-Liouville problem
نویسندگان
1 Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran.
2 Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran.
3 Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran.
4 Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran.
doi
10.22034/cmde.2023.57436.2403چکیده
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 $O(n^2h^2)$.
