Line integral solution of Hamiltonian systems with holonomic constraints

作者: Luigi Brugnano , Gianmarco Gurioli , Felice Iavernaro , Ewa B. Weinmüller

DOI: 10.1016/J.APNUM.2017.12.014

关键词:

摘要: Abstract In this paper, we propose a second order energy-conserving approximation procedure for Hamiltonian systems with holonomic constraints. The derivation of the relies on use so-called line integral framework . We provide numerical experiments to illustrate theoretical findings.

参考文章(41)
Luigi Brugnano, Felice Iavernaro, Donato Trigiante, A two-step, fourth-order method with energy preserving properties Computer Physics Communications. ,vol. 183, pp. 1860- 1868 ,(2012) , 10.1016/J.CPC.2012.04.002
Werner M. Seiler, Position versus momentum projections for constrained Hamiltonian systems Numerical Algorithms. ,vol. 19, pp. 223- 234 ,(1998) , 10.1023/A:1019170926730
Luigi Brugnano, Felice Iavernaro, Donato Trigiante, A simple framework for the derivation and analysis of effective one-step methods for ODEs Applied Mathematics and Computation. ,vol. 218, pp. 8475- 8485 ,(2012) , 10.1016/J.AMC.2012.01.074
Luigi Brugnano, Felice Iavernaro, Donato Trigiante, Energy- and Quadratic Invariants--Preserving Integrators Based upon Gauss Collocation Formulae SIAM Journal on Numerical Analysis. ,vol. 50, pp. 2897- 2916 ,(2012) , 10.1137/110856617
L. Brugnano, G. Frasca Caccia, F. Iavernaro, Energy conservation issues in the numerical solution of the semilinear wave equation Applied Mathematics and Computation. ,vol. 270, pp. 842- 870 ,(2015) , 10.1016/J.AMC.2015.08.078
Luigi Brugnano, Gianluca Frasca Caccia, Felice Iavernaro, Efficient implementation of Gauss collocation and Hamiltonian boundary value methods Numerical Algorithms. ,vol. 65, pp. 633- 650 ,(2014) , 10.1007/S11075-014-9825-0
Hans C Andersen, Rattle: A “velocity” version of the shake algorithm for molecular dynamics calculations Journal of Computational Physics. ,vol. 52, pp. 24- 34 ,(1983) , 10.1016/0021-9991(83)90014-1
Sebastian Reich, Symplectic integration of constrained Hamiltonian systems by composition methods SIAM Journal on Numerical Analysis. ,vol. 33, pp. 475- 491 ,(1996) , 10.1137/0733025