Energy-preserving methods for Poisson systems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:236

Article

Brugnano, L.²  Calvo, M.¹  Montijano, J. I.¹  Randez, L.¹ 

[1] Univ Zaragoza, IUMA Dept Matemat Aplicada, E-50009 Zaragoza, Spain

[2] Univ Florence, Dipartimento Matemat U Dini, I-50121 Florence, Italy

关键词: Ordinary differential equations;    One-step methods;    Poisson problems;    Hamiltonian boundary value methods;    Energy-preserving methods;    Line integral methods;   

DOI  :  10.1016/j.cam.2012.02.033

来源: Elsevier

【 摘 要 】

We present and analyze energy-conserving methods for the numerical integration of IVPs of Poisson type that are able to preserve some Casimirs. Their derivation and analysis is done following the ideas of Hamiltonian BVMs (HBVMs) (see Brugnano et al. [10] and references therein). It is seen that the proposed approach allows us to obtain the methods recently derived in Cohen and Hairer (2011) [17], giving an alternative derivation of such methods and a new proof of their order. Sufficient conditions that ensure the existence of a unique solution of the implicit equations defining the formulae are given. A study of the implementation of the methods is provided. In particular, order and preservation properties when the involved integrals are approximated by means of a quadrature formula, are derived. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free