Chin. Phys. Lett.  2011, Vol. 28 Issue (7): 070201    DOI: 10.1088/0256-307X/28/7/070201
GENERAL |
Two New Fourth-Order Three-Stage Symplectic Integrators
LI Rong, WU Xin**
School of Science, Nanchang University, Nanchang 330031
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LI Rong, WU Xin 2011 Chin. Phys. Lett. 28 070201
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Abstract Two new fourth-order three-stage symplectic integrators are specifically designed for a family of Hamiltonian systems, such as the harmonic oscillator, mathematical pendulum and lattice φ4 model. When the nonintegrable lattice φ4 system is taken as a test model, numerical comparisons show that the new methods have a great advantage over the second-order Verlet symplectic integrators in the accuracy of energy, become explicitly better than the usual non-gradient fourth-order seven-stage symplectic integrator of Forest and Ruth, and are almost equivalent to a fourth-order seven-stage force gradient symplectic integrator of Chin. As the most important advantage, the new integrators are convenient for solving the variational equations of many Hamiltonian systems so as to save a great deal of the computational cost when scanning a lot of orbits for chaos.
Keywords: 02.70.-c      05.10.-a      45.10.-b     
Received: 04 March 2011      Published: 29 June 2011
PACS:  02.70.-c (Computational techniques; simulations)  
  05.10.-a (Computational methods in statistical physics and nonlinear dynamics)  
  45.10.-b (Computational methods in classical mechanics)  
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https://cpl.iphy.ac.cn/10.1088/0256-307X/28/7/070201       OR      https://cpl.iphy.ac.cn/Y2011/V28/I7/070201
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Articles by authors
LI Rong
WU Xin
[1] Feng K 1986 J. Comput. Math. 4 279
[2] Zhong S Y, Wu X, Liu S Q and Deng X F 2010 Phys. Rev. D 82 124040
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[6] Yoshida H 1990 Phys. Lett. A 150 262
[7] Ruth R D 1983 IEEE Trans. Nucl. Sci. 30 2669
[8] Li R and Wu X 2010 Sci. Chin. Phys. Mech. Astron. 53 1600
[9] Chin S A 1997 Phys. Lett. A 226 344
[10] Li R and Wu X 2010 Acta. Phys. Sin. 59 7135 (in Chinese)
[11] Sun W, Wu X and Huang G Q 2011 Res. Astron. Astrophys. 11 353
[12] Xu J and Wu X 2010 Res. Astron. Astrophys. 10 173
[13] Chin S A 2009 Phys. Rev. E 80 037701
[14] Forest E and Ruth R D 1990 Physica D 43 105
[15] Pettini M, Casetti L, Cerruti-Sola M, Franzosi R and Cohen E G D 2005 Chaos 15 015016
[16] Wu X, Huang T Y and Zhang H 2006 Phys. Rev. D 74 083001
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