Abstract
The aim of this section is to study convergence of multistep methods when applied to singular perturbation problems (Runge-Kutta methods will be treated in Sect. VI.3). We are interested in estimates that hold uniformly for ε → 0. The results of the previous chapters cannot be applied. Since the Lipschitz constant of the singular perturbation problem (1.5) is of size O(ε −1), the estimates of Sect. 111.4 are useless. Also the one-sided Lipschitz constant is in general O(ε −1), so that the convergence results of Sect. V.8 can neither be applied. Let us start by considering the reduced problem.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Hairer, E., Wanner, G. (1996). Multistep Methods. In: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05221-7_26
Download citation
DOI: https://doi.org/10.1007/978-3-642-05221-7_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05220-0
Online ISBN: 978-3-642-05221-7
eBook Packages: Springer Book Archive