Optimized third-order force-gradient symplectic algorithms  

作　　者：LI Rong & WU Xin School of Science,Nanchang University,Nanchang 330031,China 

出　　处：《Science China(Physics,Mechanics & Astronomy)》2010年第9期1600-1609,共10页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the NationalNatural Science Foundation of China (Grant No.10873007);supported by the Science Foundation of Jiangxi Education Bureau (Grant No.GJJ09072);the Program for Innovative Research Team of Nanchang University

摘　　要：With the natural splitting of a Hamiltonian system into kinetic energy and potential energy,we construct two new optimal thirdorder force-gradient symplectic algorithms in each of which the norm of fourth-order truncation errors is minimized.They are both not explicitly superior to their no-optimal counterparts in the numerical stability and the topology structure-preserving,but they are in the accuracy of energy on classical problems and in one of the energy eigenvalues for one-dimensional time-independent Schrdinger equations.In particular,they are much better than the optimal third-order non-gradient symplectic method.They also have an advantage over the fourth-order non-gradient symplectic integrator.With the natural splitting of a Hamiltonian system into kinetic energy and potential energy,we construct two new optimal thirdorder force-gradient symplectic algorithms in each of which the norm of fourth-order truncation errors is minimized.They are both not explicitly superior to their no-optimal counterparts in the numerical stability and the topology structure-preserving,but they are in the accuracy of energy on classical problems and in one of the energy eigenvalues for one-dimensional time-independent Schrdinger equations.In particular,they are much better than the optimal third-order non-gradient symplectic method.They also have an advantage over the fourth-order non-gradient symplectic integrator.

关 键 词：SYMPLECTIC INTEGRATORS SYMPLECTIC scheme-shooting METHOD celestial mechanics time-independent Schrdinger equation energy eigenvalues numerical stability BISECTION METHOD topological structure 

分 类 号：O302[理学—力学]