A numerically rigorous proof of curve veering in an eigenvalue problem for differential equations

DOI10.4171/ZAA/694zbMath0873.65080OpenAlexW2075722660MaRDI QIDQ1909649

H. Behnke

Publication date: 12 October 1997

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/zaa/694

zbMATH Keywords

interval arithmeticeigenvalue curvescurve veeringparameter-dependent selfadjoint eigenvalue problemssystems of ordinary fourth-order differential equations

Mathematics Subject Classification ID

Interval and finite arithmetic (65G30) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) 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 (5)

On the convergence of the Goerisch method for self-adjoint eigenvalue problems with arbitrary spectrum ⋮ Eigenwertschranken für das Problem der frei schwingenden rechteckigen Platte und Untersuchungen zum Ausweichphänomen ⋮ NUMERICAL VERIFICATION METHODS FOR SOLUTIONS OF ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS ⋮ An efficient direct solver for a class of mixed finite element problems ⋮ Curve Veering for the Parameter-dependent Clamped Plate

Uses Software

• Mathematica

Cites Work

• The calculation of guaranteed bounds for eigenvalues using complementary variational principles
• Bounds for eigenvalues of parameter-dependent matrices
• Variational bounds to eigenvalues of selfadjoint eigenvalue problems with arbitrary spectrum
• Optimale Eigenwerteinschließungen
• Eigenwertschranken für Eigenwertaufgaben mit partiellen Differentialgleichungen
• [https://portal.mardi4nfdi.de/wiki/Publication:3899612 Zum Einflu� des Schwingungsverhaltens eines scheibenf�rmigen Tragk�rpers auf die Eigenfrequenzen der Schaufeln thermischer Turbomaschinen]
• Interval Methods for Systems of Equations
• Eigenwertschranken für das Problem der frei schwingenden rechteckigen Platte und Untersuchungen zum Ausweichphänomen
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