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Tensor invariants in numerical geometric integration of ODEs
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Arponen, Teijo (2007) Tensor invariants in numerical geometric integration of ODEs. Journal of Computational and Applied Mathematics, Vol.205 (No.2). pp. 791-801. doi:10.1016/j.cam.2006.03.037 ISSN 0377-0427.
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Official URL: http://dx.doi.org/10.1016/j.cam.2006.03.037
Abstract
We consider geometric numerical integration (GI) of ordinary differential equations (ODEs). We propose that in GI one needs concepts which are both geometric and algebraic. In this paper we start from an algebraic point of view: we introduce tensor invariants attached to an ODE as well as to an integrator. The notion of "sharing a tensor invariant" generalizes the well known notion of conserving a symplectic structure by an integrator. Several examples are given. (c) 2006 Elsevier B.V. All rights reserved.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Journal of Computational and Applied Mathematics | ||||
| Publisher: | Elseivier Science BV | ||||
| ISSN: | 0377-0427 | ||||
| Official Date: | 15 August 2007 | ||||
| Dates: |
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| Volume: | Vol.205 | ||||
| Number: | No.2 | ||||
| Number of Pages: | 11 | ||||
| Page Range: | pp. 791-801 | ||||
| DOI: | 10.1016/j.cam.2006.03.037 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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