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 $O(n^2h^2)$.
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Mirzaei, H., Emami, M., Ghanbari, K., & Shahriari, M. (2024). An efficient algorithm for computing the eigenvalues of conformable Sturm-Liouville problem. Computational Methods for Differential Equations, 12(3), 471-483. doi: 10.22034/cmde.2023.57436.2403
MLA
Hanif Mirzaei; Mahmood Emami; Kazem Ghanbari; Mohammad Shahriari. "An efficient algorithm for computing the eigenvalues of conformable Sturm-Liouville problem". Computational Methods for Differential Equations, 12, 3, 2024, 471-483. doi: 10.22034/cmde.2023.57436.2403
HARVARD
Mirzaei, H., Emami, M., Ghanbari, K., Shahriari, M. (2024). 'An efficient algorithm for computing the eigenvalues of conformable Sturm-Liouville problem', Computational Methods for Differential Equations, 12(3), pp. 471-483. doi: 10.22034/cmde.2023.57436.2403
VANCOUVER
Mirzaei, H., Emami, M., Ghanbari, K., Shahriari, M. An efficient algorithm for computing the eigenvalues of conformable Sturm-Liouville problem. Computational Methods for Differential Equations, 2024; 12(3): 471-483. doi: 10.22034/cmde.2023.57436.2403
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