求解振荡哈密顿系统的相拟合辛PRK方法(英文)  

PHASE-FITTED SYMPLECTIC PRK METHODS FOR OSCILLATORY HAMILTONIAN SYSTEMS

作　　者：陈朝霞[1] 石磊[1] 游雄[1,2] 

机构地区：[1]南京农业大学数学系,南京210095 [2]南京大学计算机软件新技术国家重点实验室,南京210093

出　　处：《南京大学学报（数学半年刊）》2012年第2期139-154,共16页Journal of Nanjing University(Mathematical Biquarterly)

基　　金：Supported by NSF of China(No11171155);the Fundamental Research Fund for the Central Universities(NoY0201100265);Youth Science and Technology Innovation Fund of Nanjing Agriculture University(NoKJ2010026)

摘　　要：研究求解可分哈密顿系统的相拟合辛PRK(FSPRK)方法.给出了修正PRK方法的代数阶条件、辛条件及相拟合与振幅拟合条件.构造了一个2级2阶和一个3级3阶FSPRK方法.对经典力学和量子力学的几个著名问题实验的数值结果证明,新的三阶方法在保持哈密顿能量与计算效率方面优于文献中的一些高效方法.Phase-fitted symplectic PRK （FSPRK） methods for separable Hamilto- nian systems are investigated. Algebraic order conditions, symplecticity conditions and phase-fitting and amplification-fitting conditions for modified PRK methods are presented. A two-stage FSPRK method of order two and a three-stage FSPRK method of order three are constructed. The numerical results of experiments on several famous testing problems in classical and quantum mechanics show that the new method of order three is superior to some highly efficient integrators in the literature in preserving the Hamiltonian energy and in efficiency.

关 键 词：辛PRK方法 哈密顿系统 相拟合 振幅拟合 

分 类 号：O241.8[理学—计算数学]