A numerically rigorous proof of curve veering in an eigenvalue problem for differential equations
type: Item
instance of: scholarly article
title: A numerically rigorous proof of curve veering in an eigenvalue problem for differential equations
zbMATH Open document ID: 0873.65080
DOI: 10.4171/ZAA/694
author: Henning Behnke
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1997-10-12T00:00:00Z
review text: Parameter-dependent selfadjoint eigenvalue problems for a system of ordinary fourth-order differential equations are considered. The phenomenon of eigenvalue curves veering is investigated by the use of numerical procedures. The author proposes such methods of computing bounds of the form \[ p(\Omega)-\epsilon \leq \lambda(\Omega) \leq p(\Omega)+\epsilon \] for the eigenvalue curves \(\lambda(\Omega)\) that rounding errors are rigorously controlled by the use of interval arithmetic. By means of calculated bounds, the phenomenon of curve veering for a concrete situation can be proved without requiring special properties of the eigenvalue curves.
Mathematics Subject Classification ID: 65L15
Mathematics Subject Classification ID: 65G30
Mathematics Subject Classification ID: 34L15
Mathematics Subject Classification ID: 65L60
zbMATH DE Number: 856812
zbMATH Keywords: parameter-dependent selfadjoint eigenvalue problems
zbMATH Keywords: systems of ordinary fourth-order differential equations
zbMATH Keywords: curve veering
zbMATH Keywords: interval arithmetic
zbMATH Keywords: eigenvalue curves
reviewed by: Teresa Regińska
describes a project that uses: Mathematica
MaRDI profile type: Publication
cites work: Q3813145
cites work: The calculation of guaranteed bounds for eigenvalues using complementary variational principles
cites work: Bounds for eigenvalues of parameter-dependent matrices
cites work: Q4321540
cites work: Eigenwertschranken für das Problem der frei schwingenden rechteckigen Platte und Untersuchungen zum Ausweichphänomen
cites work: Q3891689
cites work: Q3675430
cites work: Eigenwertschranken für Eigenwertaufgaben mit partiellen Differentialgleichungen
cites work: Q3350724
cites work: Zum Einflu� des Schwingungsverhaltens eines scheibenf�rmigen Tragk�rpers auf die Eigenfrequenzen der Schaufeln thermischer Turbomaschinen
cites work: Q5792267
cites work: Optimale Eigenwerteinschließungen
cites work: Q3774852
cites work: Interval Methods for Systems of Equations
cites work: Q3707258
cites work: Q3813151
cites work: Q3823708
cites work: Variational bounds to eigenvalues of selfadjoint eigenvalue problems with arbitrary spectrum
full work available at URL: https://doi.org/10.4171/zaa/694
OpenAlex ID: W2075722660
description: scientific article; zbMATH DE number 856812