SpectrUW: a laboratory for the numerical exploration of spectra of linear operators

DOI10.1016/j.matcom.2006.10.011zbMath1113.65058OpenAlexW2058472500MaRDI QIDQ875338

John D. Carter, Firat Kiyak, J. Nathan Kutz, Bernard Deconinck

Publication date: 13 April 2007

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2006.10.011

zbMATH Keywords

stabilitynumerical examplesspectrumHill's methodcomputing spectrafloquet

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Numerical solutions to equations with linear operators (65J10)

Related Items (15)

Numerical continuation of boundaries in parameter space between stable and unstable periodic travelling wave (wavetrain) solutions of partial differential equations ⋮ Stability of periodic Kuramoto-Sivashinsky waves ⋮ Numerical continuation methods for studying periodic travelling wave (wavetrain) solutions of partial differential equations ⋮ Turing patterns in parabolic systems of conservation laws and numerically observed stability of periodic waves ⋮ Nonlinear modulational stability of periodic traveling-wave solutions of the generalized Kuramoto-Sivashinsky equation ⋮ The Stability Analysis of the Periodic Traveling Wave Solutions of the mKdV Equation ⋮ On the spectra of periodic waves for infinite-dimensional Hamiltonian systems ⋮ Stability of viscous St. Venant roll waves: from onset to infinite Froude number limit ⋮ Periodic finite-genus solutions of the KdV equation are orbitally stable ⋮ On the Spectral and Orbital Stability of Spatially Periodic Stationary Solutions of Generalized Korteweg-de Vries Equations ⋮ Metastability of solitary roll wave solutions of the St. Venant equations with viscosity ⋮ The modulational instability for a generalized Korteweg-de Vries equation ⋮ Parameterization Method for Unstable Manifolds of Standing Waves on the Line ⋮ Transverse Spectral Stability of Small Periodic Traveling Waves for the KP Equation ⋮ Internal solitary waves in the ocean: analysis using the periodic, inverse scattering transform

Uses Software

• SpectrUW

Cites Work

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• Computing spectra of linear operators using the Floquet-Fourier-Hill method
• Computing absolute and essential spectra using continuation
• Nonlinear stability of fluid and plasma equilibria
• Transverse instabilities of deep-water solitary waves
• The inverse scattering transform: Semi-infinite interval
• The occurrence of parametric instabilities in finite-amplitude internal gravity waves
• The linear stability of flat Stokes layers
• Parametric Resonance in Immersed Elastic Boundaries
• The linear stability of flat Stokes layers

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