Abstract
The numerical approximation of boundary value problems in the context of one-parameter continuation is considered. A collocation discretization of parameter dependent boundary value problems is suggested. The convergence properties are analysed and a stable algorithm is presented. Tangent continuation and steplength control are combined with a Gauss—Newton type corrector, which is shown to be quadratically convergent. Based on this analysis, a general purpose continuation code COLCON has been implemented. Numerical examples demonstrating the efficiency of the approach are presented.
The present work has been suppotted by the Deutsche Forschungsgemeinschaft.
This paper is published in: SIAM J. Sci. Stat. Comput.,10, 72–88, (1989)
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Kluwer Academic Publishers
About this chapter
Cite this chapter
Bader, G., Kunkel, P. (1990). Continuation and Collocation for Parameter Dependent Boundary Value Problems. In: Roose, D., Dier, B.D., Spence, A. (eds) Continuation and Bifurcations: Numerical Techniques and Applications. NATO ASI Series, vol 313. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0659-4_29
Download citation
DOI: https://doi.org/10.1007/978-94-009-0659-4_29
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6781-2
Online ISBN: 978-94-009-0659-4
eBook Packages: Springer Book Archive