Numerical solution of eigenvalue problems for Hamiltonian systems
type: Item
instance of: scholarly article
title: Numerical solution of eigenvalue problems for Hamiltonian systems
zbMATH Open document ID: 0833.65083
DOI: 10.1007/BF02521106
published in: Advances in Computational Mathematics
publication date: 1996-03-14T00:00:00Z
review text: The paper concerns an eigenvalue problem for a Hamiltonian system of ordinary differential equations with nonlinear dependence on a real eigenparameter \(\lambda\). Separated boundary conditions are treated. The coefficients are at least continuously differentiable as a function of \(\lambda\). Using \(\Theta\) matrices of Atkinson the author constructs an increasing integer-valued function \(M(\lambda)\) whose only points of increase are discontinuities at the eigenvalues, and the size of the discontinuity is equal to the multiplicity of the corresponding eigenvalue. The author describes two alternative approaches to the problem of computing the function \(M(\lambda)\). Some numerical experiments using these algorithms are presented. The author informs that both codes are fully documented and are written in Fortran 77, and will be available in netlib/aicm/sl11f and netlib/aicm/sl12f.
Mathematics Subject Classification ID: 65L15
Mathematics Subject Classification ID: 37-XX
Mathematics Subject Classification ID: 34L15
zbMATH DE Number: 784490
zbMATH Keywords: eigenvalue
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: nonlinear dependence
zbMATH Keywords: numerical experiments
author: Marco Marletta
reviewed by: Teresa Regińska
describes a project that uses: SLEDGE
describes a project that uses: Netlib
MaRDI profile type: Publication
cites work: Discrete and continuous boundary problems
cites work: Unitary Integrators and Applications to Continuous Orthonormalization Techniques
cites work: On the exponential solution of differential equations for a linear operator
cites work: Certification of algorithm 700 numerical tests of the SLEIGN software for Sturm-Liouville problems
cites work: Automatic solution of regular and singular vector Sturm-Liouville problems
cites work: Automatic solution of Sturm-Liouville problems using the Pruess method
cites work: Estimating the Eigenvalues of Sturm–Liouville Problems by Approximating the Differential Equation
cites work: Error Control of Phase-Function Shooting Methods for Sturm-Liouville Problems
cites work: Q5685430
cites work: Sturmian theory for ordinary differential equations
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description: scientific article; zbMATH DE number 784490