Invariants preserving schemes based on explicit Runge–Kutta methods

Numerical integration of ordinary differential equations with some invariants is considered. For such a purpose, certain projection methods have proved its high accuracy and efficiency. Unfortunately, however, sometimes they can exhibit instability. In this paper, a new, highly efficient projection...

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Veröffentlicht in:BIT 2016-12, Vol.56 (4), p.1317-1337
1. Verfasser: Kojima, H.
Format: Artikel
Sprache:eng
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Zusammenfassung:Numerical integration of ordinary differential equations with some invariants is considered. For such a purpose, certain projection methods have proved its high accuracy and efficiency. Unfortunately, however, sometimes they can exhibit instability. In this paper, a new, highly efficient projection method is proposed based on explicit Runge–Kutta methods. The key there is to employ the idea of the perturbed collocation method, which gives a unified way to incorporate scheme parameters for projection. Numerical experiments confirm the stability of the proposed method.
ISSN:0006-3835
1572-9125
DOI:10.1007/s10543-016-0608-y