Abstract
Convergence results of multistep methods for problems of index at least 2 are harder to obtain than for semi-explicit index 1 problems (see Section VI.2). A first convergence result for BDF schemes, valid for linear constant coefficient DAE’s of arbitrary index, was given by Sincovec, Erisman, Yip & Epton (1981). Convergence of BDF for nonlinear DAE systems was then studied by Gear, Gupta & Leimkuhler (1985), Lötstedt & Petzold (1986) and Brenan & Engquist (1988). An independent convergence analysis was given by Griepentrog & März (1986), März (1990). They considered general linear multistep methods and problems, where the differential and algebraic equations (and/or variables) are not explicitly separated.
BDF is so beautiful that it is hard to imagine something else could be better.
(L. Petzold 1988, heard by P. Deuflhard)
This is a preview of subscription content, log in via an institution to check access.
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 for Index 2 DAE. 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_33
Download citation
DOI: https://doi.org/10.1007/978-3-642-05221-7_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05220-0
Online ISBN: 978-3-642-05221-7
eBook Packages: Springer Book Archive