TY - JOUR
T1 - Several Abstract Iterative Schemes for Solving the Bifurcation at Simple Eigenvalues
AU - Zhong-Hua Yang
JO - Journal of Computational Mathematics
VL - 3
SP - 201
EP - 209
PY - 1984
DA - 1984/02
SN - 2
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/9654.html
KW - 
AB - <p style="text-align: justify;">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.</p>