Asymptotic correction of Numerov's eigenvalue estimates with natural boundary conditions

DOI10.1016/S0377-0427(00)00479-9zbMath0970.65086MaRDI QIDQ1841967

Alan L. Andrew

Publication date: 18 February 2001

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

eigenvaluesfinite elementfinite differenceregular Sturm-Liouville problemsasymptotic correction

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Finite difference and finite volume methods for ordinary differential equations (65L12) Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators (34L16) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15)

Related Items (20)

Boundary value method for inverse Sturm-Liouville problems ⋮ Approximate solution of the Sturm-Liouville problems with Legendre-Galerkin-Chebyshev collocation method ⋮ Exponentially-fitted Numerov methods ⋮ Mapped barycentric Chebyshev differentiation matrix method for the solution of regular Sturm-Liouville problems ⋮ Bvms for computing Sturm-Liouville symmetric potentials ⋮ A finite difference method for an inverse Sturm-Liouville problem in impedance form ⋮ Solving Sturm-Liouville inverse problems by an orthogonalized enhanced boundary function method and a product formula for symmetric potential ⋮ Optimal grid method for the recovery of the potential from two spectra ⋮ A new approach for linear eigenvalue problems and nonlinear Euler buckling problem ⋮ Broyden method for inverse non-symmetric Sturm-Liouville problems ⋮ Computing the eigenvalues of the generalized Sturm-Liouville problems based on the Lie-group \(SL(2,\mathbb R)\) ⋮ Matrix methods for computing eigenvalues of Sturm-Liouville problems of order four ⋮ Modified Numerov's method for inverse Sturm-Liouville problems ⋮ Convergence of Numerov's method for inverse Sturm-Liouville problems ⋮ On a modified Numerov's method for inverse Sturm–Liouville problems ⋮ Approximations of Sturm-Liouville eigenvalues using differential quadrature (DQ) method ⋮ Boundary value methods for the reconstruction of Sturm-Liouville potentials ⋮ Boundary value methods as an extension of Numerov's method for Sturm-Liouville eigenvalue estimates ⋮ Approximate computation of eigenvalues with Chebyshev collocation method ⋮ On a boundary value method for computing Sturm–Liouville potentials from two spectra

Cites Work

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• Correction of Numerov's eigenvalue estimates
• On the correction of finite difference eigenvalue approximations for Sturm-Liouville problems with general boundary conditions
• Small potential corrections for the discrete eigenvalues of the Sturm- Liouville problem
• Correction of finite element estimates for Sturm-Liouville eigenvalues
• Correction of finite element eigenvalues for problems with natural or periodic boundary conditions
• On the correction of finite difference eigenvalue approximations for Sturm-Liouville problems
• Corrected finite difference eigenvalues of periodic Sturm-Liouville problems
• Approximations of Sturm-Liouville eigenvalues using boundary value methods
• A modified difference scheme for periodic and semiperiodic Sturm- Liouville problems
• A Numerical Method for the Inverse Sturm–Liouville Problem
• Correction of finite difference eigenvalues of periodic Sturm-Liouville problems
• A finite-difference algorithm for an inverse Sturm-Liouville problem
• ASYMPTOTIC FORMULAS FOR DISCRETE EIGENVALUE PROBLEMS IN LIOUVILLE NORMAL FORM

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