Multistep methods on manifolds
Author: Iserles, A.
Source: IMA Journal of Numerical Analysis, Volume 21, Number 1, 1 January 2001 , pp. 407-419(13)
Publisher: Oxford University Press
Abstract:We explore the retention of invariants by a class of time-stepping discretization methods, inclusive of linear multistep methods and truncated Taylor expansions. Our main result is that no such method can respect invariance on a nonlinear manifold.
Keywords: manifolds, invariance, multistep methods
Document Type: Journal Article
Affiliations: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK, e-mail: A.Iserles@damtp.cam.ac.uk; www: http//www.damtp.cam.ac.uk/user/na/people/Arieh/
Publication date: 2001-01-01
- The IMA Journal of Numerical Analysis (IMAJNA) publishes original contributions to all fields of numerical analysis; articles will be accepted which treat the theory, development or use of practical algorithms and interactions between these aspects. Occasional survey articles are also published.