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 | |
| 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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Cite this
Greenlee, W. M., & Hermi, L. (2010). Quadratic interpolation and Rayleigh-Ritz methods for bifurcation coefficients. SIAM Journal on Mathematical Analysis, 42(6), 2987-3019. https://doi.org/10.1137/090750445