TY - JOUR
ID - 17114
TI - An efficient algorithm for computing the eigenvalues of conformable Sturm-Liouville problem
JO - Computational Methods for Differential Equations
JA - CMDE
LA - en
SN - 2345-3982
AU - Mirzaei, Hanif
AU - Emami, Mahmood
AU - Ghanbari, Kazem
AU - Shahriari, Mohammad
AD - Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran.
AD - Department of Mathematics, Faculty of Science, University of Maragheh, Maragheh, Iran.
Y1 - 2024
PY - 2024
VL - 12
IS - 3
SP - 471
EP - 483
KW - Sturm-Liouville problem
KW - Conformable derivative
KW - Finite elements method
KW - Correction idea
DO - 10.22034/cmde.2023.57436.2403
N2 - 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 $O(n^2h^2)$.
UR - https://cmde.tabrizu.ac.ir/article_17114.html
L1 - https://cmde.tabrizu.ac.ir/article_17114_243b85e9d190741b80f2ad25cd182df0.pdf
ER -