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

作     者：Lei Li Dongling Wang 

作者机构：School of Mathematical SciencesInstitute of Natural SciencesMOE-LSCShanghai Jiao Tong UniversityShanghai 200240China School of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105China 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2023年第41卷第1期

页      面：107-132页

核心收录：

学科分类：083002[工学-环境工程] 0830[工学-环境科学与工程（可授工学、理学、农学学位）] 08[工学] 

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 

主　　题：Hamiltonian systems Holonomic constraints symplecticity Quadratic invariants Partitioned Runge-Kutt methods 

摘      要：We introduce a new class of parametrized structure–preserving partitioned RungeKutta(α-PRK)methods for Hamiltonian systems with holonomic *** 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=*** 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 ***,for any given consistent initial values(p0,q0)and small step size h0,it is proved that there existsα∗=α(h,p0,q0)such that the Hamiltonian energy can also be exactly preserved at each *** on this,we propose some energy and quadratic invariants preservingα-PRK ***α-PRK methods are shown to have the same convergence rate as the usual PRK methods and perform very well in various numerical experiments.