Automatic solution of regular and singular vector Sturm-Liouville problems

DOI10.1007/BF02142741zbMath0820.65050MaRDI QIDQ1208057

Marco Marlettta

Publication date: 16 May 1993

Published in: Numerical Algorithms (Search for Journal in Brave)

zbMATH Keywords

algorithmseigenvaluesspectral functionsingular problemsmiss-distance functionvector Sturm-Liouville problems

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Related Items (11)

Classical and vector Sturm-Liouville problems: Recent advances in singular-point analysis and shooting-type algorithms ⋮ Improvements to the computation of eigenvalues and eigenfunctions of two-dimensional Schrödinger equations by constant perturbation based algorithms ⋮ Numerical solution of eigenvalue problems for Hamiltonian systems ⋮ Numerical computation of eigenvalues in spectral gaps of Schrödinger operators ⋮ On the eigenvalues of spectral gaps of matrix-valued Schrödinger operators ⋮ New numerical method for the eigenvalue problem of the 2D Schrödinger equation ⋮ A numerical procedure to solve the multichannel Schrödinger eigenvalue problem ⋮ Spectral corrections for Sturm-Liouville problems ⋮ Eigenvalue problem for a coupled channel Schrödinger equation with application to the description of deformed nuclear systems ⋮ Eigenvalues of vectorial Sturm-Liouville problems with parameter dependent boundary conditions ⋮ Sampling the miss-distance and transmission function

Uses Software

• SLEIGN

Cites Work

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• Numerical solution of a system of integrodifferential equations arising from the quantum mechanical three-body problem with Coulomb interaction
• Choosing step sizes for perturbative methods of solving the Schrödinger equation
• Sturmian theory for ordinary differential equations
• Automatic solution of Sturm-Liouville problems using the Pruess method
• The error analysis of the algebraic method for solving the Schrödinger equation
• Discrete and continuous boundary problems
• Halbbeschränkte gewöhnliche Differentialoperatoren zweiter Ordnung
• Error Control of Phase-Function Shooting Methods for Sturm-Liouville Problems
• Certification of algorithm 700 numerical tests of the SLEIGN software for Sturm-Liouville problems
• Applications of functional analysis and operator theory

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