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IMA Journal of Numerical Analysis 2001 21(1):407-419; doi:10.1093/imanum/21.1.407
© 2001 by Institute of Mathematics and its Applications
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Multistep methods on manifolds

Arieh Iserles1

1 Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK, e-mail: A.Iserles{at}damtp.cam.ac.uk; www: http//www.damtp.cam.ac.uk/user/na/people/Arieh/

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.

Key Words: manifolds, invariance, multistep methods

Received 15 July 1997. Accepted 27 January 2000.


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