Analysis of Energy and QUadratic Invariant Preserving (EQUIP) methods

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:335

Article

Brugnano, Luigi¹  Gurioli, Gianmarco¹  Iavernaro, Felice² 

[1] Dipartimento Matemat & Informat U Dini, Viale Morgagni 67-A, I-50134 Florence, Italy

[2] Dipartimento Matemat, Via Orabona 4, I-70125 Bari, Italy

关键词: Gauss collocation methods;    Symplectic methods;    Energy-conserving methods;    Line integral methods;    Hamiltonian problems;    Poisson problems;   

DOI  :  10.1016/j.cam.2017.11.043

来源: Elsevier

【 摘 要 】

In this paper we are concerned with the analysis of a class of geometric integrators, at first devised in Brugnano et al. (2010) and Brugnano et al. (2012), which can be regarded as an energy-conserving variant of Gauss collocation methods. With these latter they share the property of conserving quadratic first integrals but, in addition, they also conserve the Hamiltonian function itself. We here reformulate the methods in a more convenient way, and propose a more refined analysis than that given in Brugnano et al. (2012) also providing, as a by-product, a practical procedure for their implementation. A thorough comparison with the original Gauss methods is carried out by means of a few numerical tests solving Hamiltonian and Poisson problems. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free