Computing Eigenfunctions of Singular Points in Nonlinear Parametrized Two-Point BVPs

by    M. Hermann, Th. Milde

Preprint series: 06-22, Reports on Numerical Mathematics

M. Hermann, Th. Milde

65L10 Boundary value problems
65P30 Bifurcation problems

Abstract: The iterative computation of singular points in parametrized nonlinear BVPs by so-called extended systems requires good starting values for the singular point itself and the corresponding eigenfunction. Using path-following techniques such starting values for the singular points should be generated automatically. However, pathfollowing does not provide approximations for the eigenfunctions. We propose a new modification of this standard technique delivering such starting values. It is based on an extended system by which singular as well as nonsingular points can be determined.

Keywords: Boundary value problem, bifurcation points, turning points, path-following, augmented systems

Upload: 2006-12-01

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