Quadratic interpolation and Rayleigh-Ritz methods for bifurcation coefficients

W. M. Greenlee, L. Hermi

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)2987-3019
Number of pages33
JournalSIAM Journal on Mathematical Analysis
Volume42
Issue number6
DOIs
StatePublished - 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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