Recent Advances on Preserving Methods for Poisson Systems

被引：0

作者：

Brugnano, L. ^{[1
]}

Calvo, M. ^{[2
]}

Montijano, J. I. ^{[2
]}

Randez, L. ^{[2
]}

机构：

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

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

来源：

NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS A-C | 2011年 / 1389卷

关键词：

Ordinary differential equations; one-step methods; Poisson problems; Hamiltonian Boundary Value Methods; energy-preserving methods; line integral methods;

D O I：

10.1063/1.3636709

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present and analyze energy-conserving methods for the numerical integration of IVPs of Poisson type systems. They are also able to preserve some Casimirs. Their derivation and analysis is done following the ideas of Hamiltonian BVMs (HBVMs) (see [3] and references therein). The proposed methods turn out to be equivalent to those recently derived in [8], giving therefore an alternative point of view that provides additional insight on the methods. 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.

引用

页数：4

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