@Article{JCM-41-107,
author = {Li , Lei and Wang , Dongling},
title = {Energy and Quadratic Invariants Preserving Methods for Hamiltonian Systems with Holonomic Constraints},
journal = {Journal of Computational Mathematics},
year = {2022},
volume = {41},
number = {1},
pages = {107--132},
abstract = {<p style="text-align: justify;">We introduce a new class of parametrized structure--preserving partitioned Runge-Kutta ($\alpha$-PRK) methods for Hamiltonian systems with holonomic constraints.&nbsp; The methods are symplectic for any fixed scalar parameter $\alpha$, and are reduced to the usual symplectic PRK methods like Shake-Rattle method or PRK schemes based on Lobatto IIIA-IIIB pairs when $\alpha=0$. We provide a new variational formulation for symplectic PRK schemes and use it to prove that the $\alpha$-PRK methods can preserve the quadratic invariants for Hamiltonian systems subject to holonomic constraints. Meanwhile, for any given consistent initial values $(p_{0}, q_0)$ and small step size $h&gt;0$, it is proved that there exists $\alpha^*=\alpha(h, p_0, q_0)$ such that the Hamiltonian energy can also be exactly preserved at each step. Based on this, we propose some energy and quadratic invariants preserving $\alpha$-PRK methods. These $\alpha$-PRK methods are shown to have the same convergence rate as the usual PRK methods and perform very well in various numerical experiments.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2106-m2020-0205},
url = {http://global-sci.org/intro/article_detail/jcm/21172.html}
}