Several Abstract Iterative Schemes for Solving the Bifurcation at Simple Eigenvalues

Several Abstract Iterative Schemes for Solving the Bifurcation at Simple Eigenvalues

Year:    1984

Journal of Computational Mathematics, Vol. 2 (1984), Iss. 3 : pp. 201–209

Abstract

In this paper we consider the nonlinear operator equation $\lambda x=Lx+G(\lambda,x)$ where $L$ is a closed linear operator of $X-›X, X$ is a real Banach Space, with a simple eigenvalue $\lambda_0\neq 0$. We discretize its Liapunov-Schmidt bifurcation equation instead of the original nonlinear operator equation and estimate the approximating order of our approximate solution to the genuine solution. Our method is more convenient and more accurate. Meanwhile we put forward several abstract Newton-type iterative schemes, which are more efficient for practical computation, and get the result of their super-linear convergence.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/1984-JCM-9654

Journal of Computational Mathematics, Vol. 2 (1984), Iss. 3 : pp. 201–209

Published online:    1984-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    9

Keywords: