Quadratic interpolation and Rayleigh-Ritz methods for bifurcation coefficients

W. M. Greenlee; L. Hermi

doi:10.1137/090750445

Quadratic interpolation and Rayleigh-Ritz methods for bifurcation coefficients

W. M. Greenlee, L. Hermi

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this article we study the estimation of bifurcation coefficients in nonlinear branching problems by means of Rayleigh-Ritz approximation to the eigenvectors of the corresponding linearized problem. It is essential that the approximations converge in a norm of sufficient strength to render the nonlinearities continuous. Quadratic interpolation between Hilbert spaces is used to seek sharp rate of convergence results for bifurcation coefficients. Examples from ordinary and partial differential problems are presented.

Original language	English (US)
Pages (from-to)	2987-3019
Number of pages	33
Journal	SIAM Journal on Mathematical Analysis
Volume	42
Issue number	6
DOIs	https://doi.org/10.1137/090750445
State	Published - Dec 1 2010

Keywords

Bifurcation
Eigenfunction approximation
Eigenvalue asymptotics
Fractional Rayleigh-RitzConvergence rates
Harmonic Ritz
Nonlinear rotating string
Quadratic interpolation

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

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keywords = "Bifurcation, Eigenfunction approximation, Eigenvalue asymptotics, Fractional Rayleigh-RitzConvergence rates, Harmonic Ritz, Nonlinear rotating string, Quadratic interpolation",

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AU - Hermi, L.

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N2 - In this article we study the estimation of bifurcation coefficients in nonlinear branching problems by means of Rayleigh-Ritz approximation to the eigenvectors of the corresponding linearized problem. It is essential that the approximations converge in a norm of sufficient strength to render the nonlinearities continuous. Quadratic interpolation between Hilbert spaces is used to seek sharp rate of convergence results for bifurcation coefficients. Examples from ordinary and partial differential problems are presented.

AB - In this article we study the estimation of bifurcation coefficients in nonlinear branching problems by means of Rayleigh-Ritz approximation to the eigenvectors of the corresponding linearized problem. It is essential that the approximations converge in a norm of sufficient strength to render the nonlinearities continuous. Quadratic interpolation between Hilbert spaces is used to seek sharp rate of convergence results for bifurcation coefficients. Examples from ordinary and partial differential problems are presented.

KW - Bifurcation

KW - Eigenfunction approximation

KW - Eigenvalue asymptotics

KW - Fractional Rayleigh-RitzConvergence rates

KW - Harmonic Ritz

KW - Nonlinear rotating string

KW - Quadratic interpolation

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JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

SN - 0036-1410

IS - 6

ER -

Quadratic interpolation and Rayleigh-Ritz methods for bifurcation coefficients

Abstract

Keywords

ASJC Scopus subject areas

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