Tensor invariants in numerical geometric integration of ODEs

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:205

Article

Arponen, Teijo

关键词: one-step methods;    dissipative system;    composition;    decomposition;   

DOI  :  10.1016/j.cam.2006.03.037

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free