\(QR\) methods and error analysis for computing Lyapunov and Sacker--Sell spectral intervals for linear differential-algebraic equations

DOI10.1007/s10444-010-9156-1zbMath1242.65150OpenAlexW2140341464MaRDI QIDQ652576

Volker Mehrmann, Erik S. Van Vleck, Vu Hoang Linh

Publication date: 14 December 2011

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-010-9156-1

zbMATH Keywords

numerical exampleserror analysisLyapunov exponentsexponential dichotomydifferential-algebraic equationstrangeness indexSacker-Sell spectrumSteklov functionQR algorithmssmooth \(QR\) factorizationspectral interval

Mathematics Subject Classification ID

Implicit ordinary differential equations, differential-algebraic equations (34A09) Characteristic and Lyapunov exponents of ordinary differential equations (34D08) Error bounds for numerical methods for ordinary differential equations (65L70) Numerical investigation of stability of solutions to ordinary differential equations (65L07) Numerical methods for differential-algebraic equations (65L80) Dichotomy, trichotomy of solutions to ordinary differential equations (34D09)

Related Items

Runge-Kutta methods revisited for a class of structured strangeness-free differential-algebraic equations, Adjoint pairs of differential-algebraic equations and their Lyapunov exponents, Control of port-Hamiltonian differential-algebraic systems and applications, Efficient integration of strangeness-free non-stiff differential-algebraic equations by half-explicit methods, Robust Stability of Differential-Algebraic Equations, Necessary and Sufficient Conditions for the Noninvertibility of Fundamental Solution Matrices of a Discontinuous System, Stable numerical solution for a class of structured differential-algebraic equations by linear multistep methods

Uses Software

• GELDA
• RODAS
• Modelica

Cites Work

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