ENERGY AND QUADRATIC INVARIANTS PRESERVING METHODS FOR HAMILTONIAN SYSTEMS WITH HOLONOMIC CONSTRAINTS  

作　　者：Lei Li Dongling Wang 

机构地区：[1]School of Mathematical Sciences,Institute of Natural Sciences,MOE-LSC,Shanghai Jiao Tong University,Shanghai 200240,China [2]School of Mathematics and Computational Science,Xiangtan University,Xiangtan 411105,China

出　　处：《Journal of Computational Mathematics》2023年第1期107-132,共26页计算数学（英文）

基　　金：sponsored by NSFC 11901389,Shanghai Sailing Program 19YF1421300 and NSFC 11971314;The work of D.Wang was partially sponsored by NSFC 11871057,11931013.

摘　　要：We introduce a new class of parametrized structure–preserving partitioned RungeKutta(α-PRK)methods for Hamiltonian systems with holonomic constraints.The methods are symplectic for any fixed scalar parameterα,and are reduced to the usual symplectic PRK methods like Shake-Rattle method or PRK schemes based on Lobatto IIIA-IIIB pairs whenα=0.We provide a new variational formulation for symplectic PRK schemes and use it to prove that theα-PRK methods can preserve the quadratic invariants for Hamiltonian systems subject to holonomic constraints.Meanwhile,for any given consistent initial values(p0,q0)and small step size h>0,it is proved that there existsα∗=α(h,p0,q0)such that the Hamiltonian energy can also be exactly preserved at each step.Based on this,we propose some energy and quadratic invariants preservingα-PRK methods.Theseα-PRK methods are shown to have the same convergence rate as the usual PRK methods and perform very well in various numerical experiments.

关 键 词：Hamiltonian systems Holonomic constraints SYMPLECTICITY Quadratic invariants Partitioned Runge-Kutt methods 

分 类 号：X70[环境科学与工程—环境工程]