TITLE

BIFURCATION ANALYSIS OF NONLINEAR PARAMETERIZED TWO-POINT BVPS WITH LIAPUNOV — SCHMIDT REDUCED FUNCTIONS

AUTHOR(S)
Hermann, M.; Milde, Th.
PUB. DATE
October 2008
SOURCE
Computational Methods in Applied Mathematics;2008, Vol. 8 Issue 4, p350
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
In this paper, we study nonlinear two-point boundary value problems (BVPs) which depend on an external control parameter. In order to determine numerically the singular points (turning or bifurcation points) of such a problem with so-called extended systems and to realize branch switching, some information on the type of the singularity is required. In this paper, we propose a strategy to gain numerically this information. It is based on strongly equivalent approximations of the corresponding Liapunov — Schmidt reduced function which are generated by a simplified Newton method. The graph of the reduced function makes it possible to determine the type of singularity. The efficiency of our numerical-graphical technique is demonstrated for two BVPs.
ACCESSION #
36085238

 

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