Analysis of Energy and QUadratic Invariant Preserving (EQUIP) methods

被引：23

作者：

Brugnano, Luigi ^{[1
]}

Gurioli, Gianmarco ^{[1
]}

Iavernaro, Felice ^{[2
]}

机构：

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

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

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2018年 / 335卷

关键词：

Gauss collocation methods; Symplectic methods; Energy-conserving methods; Line integral methods; Hamiltonian problems; Poisson problems; HAMILTONIAN BOUNDARY-VALUE; RUNGE-KUTTA SCHEMES; NUMERICAL-SOLUTION; CONSERVING METHODS; GAUSS COLLOCATION; CONSERVATION; INTEGRATORS; HBVMS;

D O I：

10.1016/j.cam.2017.11.043

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页码：51 / 73

页数：23

共 37 条

[1] Energy-conserving methods for Hamiltonian boundary value problems and applications in astrodynamics [J].

Amodio, Pierluigi ;

Brugnano, Luigi ;

Iavernaro, Felice .

ADVANCES IN COMPUTATIONAL MATHEMATICS, 2015, 41 (04) :881-905

[2]

[Anonymous], 2008, NUMERICAL METHODS SC

[3]

[Anonymous], 1996, SPRINGER SER COMPUT

[4] Energy-conserving methods for the nonlinear Schrodinger equation [J].

Barletti, L. ;

Brugnano, L. ;

Frasca Caccia, Gianluca ;

Iavernaro, F. .

APPLIED MATHEMATICS AND COMPUTATION, 2018, 318 :3-18

[5]

Blanes S., 2016, CONCISE INTRO GEOMET

[6] Energy conservation issues in the numerical solution of the semilinear wave equation [J].

Brugnano, L. ;

Frasca Caccia, Gianluca ;

Iavernaro, F. .

APPLIED MATHEMATICS AND COMPUTATION, 2015, 270 :842-870

[7] Energy-preserving methods for Poisson systems [J].

Brugnano, L. ;

Calvo, M. ;

Montijano, J. I. ;

Randez, L. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2012, 236 (16) :3890-3904

[8]

Brugnano L., 2010, Monogr. Real Acad. Ci. Zaragoza, V33, P95

[9]

Brugnano L., 2016, Line integral methods for conservative problems

[10]

Brugnano L., 2010, JNAIAM J NUMER ANAL, V5, P17

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