Bifurcation Analysis Of Nonlinear Parameterized Two-Point Bvps With Liapunov — Schmidt Reduced Functions

Abstract: In this paper, we study nonlinear two-point boundary value problems (BVPs) which depend on an external control parameter. In order to determine numeri-cally 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.

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: Bifurcation Analysis Of Nonlinear Parameterized Two-Point Bvps With Liapunov — Schmidt Reduced Functions ; volume:8 ; number:4 ; year:2008 ; pages:350-359 ; Computational methods in applied mathematics ; 8, Heft 4 (2008), 350-359

Contributors, Places and Time

• Creator: HERMANN, M. ; MILDE, T.H.

Further information

• DOI: 10.2478/cmam-2008-0025
• URN: urn:nbn:de:101:1-2410261630086.108815676569
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 28.02.0003, 6:31 AM CET