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