Displaying similar documents to “Improving backward stability of Sakurai-Sugiura method with balancing technique in polynomial eigenvalue problem”

Linear stability of Euler equations in cylindrical domain

Čermák, Libor

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The linear stability problem of inviscid incompressible steady flow between two concentric cylinders is investigated. Linearizing the transient behavior around a steady state solution leads to an eigenvalue problem for linearized Euler equations. The discrete eigenvalue problem is obtained by the spectral element method. The algorithm is implemented in MATLAB. The developed program serves as a simple tool for numerical experimenting. It enables to state rough dependency of the stability...

A modified Cayley transform for the discretized Navier-Stokes equations

K. A. Cliffe, T. J. Garratt, Alastair Spence (1993)

Applications of Mathematics

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This paper is concerned with the problem of computing a small number of eigenvalues of large sparse generalized eigenvalue problems. The matrices arise from mixed finite element discretizations of time dependent equations modelling viscous incompressible flow. The eigenvalues of importance are those with smallest real part and are used to determine the linearized stability of steady states, and could be used in a scheme to detect Hopf bifurcations. We introduce a modified Cayley transform...

The effect of reduced integration in the Steklov eigenvalue problem

María G. Armentano (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper we analyze the effect of introducing a numerical integration in the piecewise linear finite element approximation of the Steklov eigenvalue problem. We obtain optimal order error estimates for the eigenfunctions when this numerical integration is used and we prove that, for singular eigenfunctions, the eigenvalues obtained using this reduced integration are better approximations than those obtained using exact integration when the mesh size is small enough.