Computing the spectral function for singular Sturm--Liouville problems

DOI10.1016/j.cam.2004.07.006zbMath1064.65075OpenAlexW2040229264MaRDI QIDQ1765364

D. B. Pearson, Charles T. Fulton, Steven A. Pruess

Publication date: 23 February 2005

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.2004.07.006

zbMATH Keywords

convergencecomparison of methodsnumerical exampleserror boundsspectral measurespectral density functionsingular Sturm-Liouville problem\(h^2\)-extrapolationMesh equidistributionsoftware package SLEDGEStep function approximation

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Stability and convergence of numerical methods for ordinary differential equations (65L20) Error bounds for numerical methods for ordinary differential equations (65L70) 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

Boundary value method for inverse Sturm-Liouville problems, Generalized polar coordinates on Lie groups and numerical integrators, The foundations of spectral computations via the solvability complexity index hierarchy, Efficient calculation of spectral density functions for specific classes of singular Sturm-Liouville problems, New characterizations of spectral density functions for singular Sturm-Liouville problems, Computing spectral measures and spectral types, A Spectral Transform Method for Singular Sturm--Liouville Problems with Applications to Energy Diffusion in Plasma Physics, Computing Spectral Measures of Self-Adjoint Operators

Uses Software

• SLEDGE

Cites Work

• Almost periodic Schrödinger operators. II: The integrated density of states
• A practical guide to splines
• On the implementation of the method of Magnus series for linear differential equations
• Eigenvalue and eigenfunction asymptotics for regular Sturm-Liouville problems
• Spectral concentration and rapidly decaying potentials
• The asymptotic nature of spectral functions in Sturm-Liouville problems with continuous spectrum
• Error analysis in the approximation of Sturm-Liouville spectral density functions
• On the global error of discretization methods for highly-oscillatory ordinary differential equations
• A simplified proof of the expansion theorem for singular second order linear differential equations
• Equidistributing Meshes with Constraints
• Solving Linear Boundary Value Problems by Approximating the Coefficients
• The computation of spectral density functions for singular Sturm-Liouville problems involving simple continuous spectra
• Computations in a free Lie algebra
• Using the SLEDGE package on Sturm-Liouville problems having nonempty essential spectra
• Mathematical software for Sturm-Liouville problems
• An Asymptotic Numerical Method for a Class of Singular Sturm–Liouville Problems
• Estimating the Eigenvalues of Sturm–Liouville Problems by Approximating the Differential Equation
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