QUADRATIC INTERPOLATION AND RAYLEIGH-RITZ METHODS FOR BIFURCATION COEFFICIENTS

被引：1

作者：

Greenlee, W. M. ^{[1
]}

Hermi, L. ^{[1
]}

机构：

[1] Univ Arizona, Dept Math, Tucson, AZ 85721 USA

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2010年 / 42卷 / 06期

关键词：

quadratic interpolation; bifurcation; fractional Rayleigh-Ritz; convergence rates; eigenfunction approximation; eigenvalue asymptotics; nonlinear rotating string; harmonic Ritz; DIFFERENTIAL-EQUATIONS; INTERMEDIATE PROBLEMS; BESSEL POTENTIALS; CONVERGENCE; EIGENVALUES;

D O I：

10.1137/090750445

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：2987 / 3019

页数：33

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