Modified Numerov's method for inverse Sturm-Liouville problems

DOI10.1016/j.cam.2013.04.025zbMath1288.65109OpenAlexW2040677800MaRDI QIDQ2453190

Qin Gao, Zhengda Huang, Xiao-liang Cheng

Publication date: 6 June 2014

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

Full work available at URL: https://doi.org/10.1016/j.cam.2013.04.025

zbMATH Keywords

interpolationSturm-Liouville operatorinverse eigenvalue problemNumerov's methodasymptotic correction

Mathematics Subject Classification ID

General spectral theory of ordinary differential operators (34L05) Inverse problems involving ordinary differential equations (34A55) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15) Numerical solution of inverse problems involving ordinary differential equations (65L09)

Related Items

Solving symmetric inverse Sturm-Liouville problem using Chebyshev polynomials ⋮ Spectrum completion and inverse Sturm–Liouville problems ⋮ Optimal grid method for the recovery of the potential from two spectra ⋮ Reconstruction techniques for complex potentials ⋮ Convergence of Numerov's method for inverse Sturm-Liouville problems ⋮ A direct method for solving inverse Sturm–Liouville problems* ⋮ On a modified Numerov's method for inverse Sturm–Liouville problems ⋮ Solving inverse Sturm–Liouville problem with separated boundary conditions by using two different input data

Cites Work

• Unnamed Item
• Unnamed Item
• Recovery of the \(m\)-function from spectral data for generalized Sturm-Liouville problems
• Bvms for computing Sturm-Liouville symmetric potentials
• Numerical solution of the inverse spectral problem for Bessel operators
• Finite difference methods for half inverse Sturm-Liouville problems
• Correction of Numerov's eigenvalue estimates
• Boundary value method for inverse Sturm-Liouville problems
• Exponentially-fitted Numerov methods
• Small potential corrections for the discrete eigenvalues of the Sturm- Liouville problem
• Multiple eigenvalue sensitivity analysis
• A convergence theorem for Newton-like methods in Banach spaces
• The inverse Sturm-Liouville problem with symmetric potentials
• On the correction of finite difference eigenvalue approximations for Sturm-Liouville problems
• Asymptotic correction of more Sturm-Liouville eigenvalue estimates.
• The eigenvalue and trace of the Sturm-Liouville operator as differentiable functions of a summable potential
• Asymptotic correction of Numerov's eigenvalue estimates with natural boundary conditions
• Matrix methods for computing eigenvalues of Sturm-Liouville problems of order four
• An Inverse Sturm–Liouville Problem with Mixed Given Data
• On the determination of a differential equation from its spectral function
• A Numerical Method for the Inverse Sturm–Liouville Problem
• A least-squares functional for solving inverse Sturm–Liouville problems
• Structured inverse eigenvalue problems
• Computing Sturm–Liouville potentials from two spectra
• The inverse Sturm–Liouville problem III
• An iterative method for the inverse Dirichlet problem
• The Inverse Sturm-Liouville Problem and the Rayleigh-Ritz Method
• Reconstruction Techniques for Classical Inverse Sturm-Liouville Problems
• The reconstruction of Sturm-Liouville operators
• The Recovery of Potentials from Finite Spectral Data
• A finite-difference algorithm for an inverse Sturm-Liouville problem
• Inverse Eigenvalue Problems
• Numerov's method for inverse Sturm–Liouville problems
• The inverse Sturm‐Liouville problem. I
• Reconstruction method for inverse Sturm–Liouville problems with discontinuous potentials
• A practical guide to splines.