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利用已存在的三阶最优化力梯度辛格式以对称组合方法获得两个新的四阶力梯度辛积分器.它们在求解摄动Kepler混沌问题的能量精度和一维定态Schrö,dinger方程的能量本征值精度方面比Forest-Ruth四阶非力梯度辛积分器要好得多,甚至还要明显优越于已有的四阶最优化力梯度辛积分器.
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关键词:
- 辛积分器 /
- 摄动Kepler问题 /
- 混沌 /
- 能量本征值
This paper provides two new fourth-order force gradient symplectic intrgrators,each of which is obtained from a symmetric product of two identied optimal third-order force gradient symplectic algorithms reported in the literature. They are both greatly superior to the fourth-order non-gradient symplectic method of Forest and Ruth in the accuracy of either energy on chaotic perturbed Kepler problems or the energy eigenvalues for one-dimensional Schrö,dinger equations. So are they to the known optimalfourth-order force gradient symplectic scheme.-
Keywords:
- symplectic integrator /
- perturbed Kepler problem /
- chaos /
- energy eigenvalues
[1] Feng K 1986 J. Comput. Math. 4 279
[2] [赵海军、 杜孟利 2007 56 3827]
[3] Ruth R D 1983 IEEE Trans. Nucl. Sci. NS-30 2669
[4] Chi Y H, Liu X S, Ding P Z 2006 Acta Phys. Sin. 55 6320 (in Chinese) [匙玉华、 刘学深、 丁培柱 2006 55 6320]
[5] Luo X Y, Liu X S, Ding P Z 2007 Acta Phys. Sin. 56 604 (in Chinese)[罗香怡、 刘学深、 丁培柱 2007 56 604]
[6] Liu X S, Wei J Y, Ding P Z 2005 Chin. Phys. 14 231
[7] Bian X B, Qiao H X, Shi T Y 2007 Chin. Phys. 16 1822
[8] Hu W P, Deng Z C 2008 Chin. Phys. B 17 3923
[9] Forest E, Ruth R D 1990 Physica D 43 105
[10] Yoshida H 1990 Phys. Lett. A 150 262
[11] Wisdom J, Holman M 1991 Astron. J. 102 1528
[12] Wisdom J, Holman M, Touma J 1996 Fields Inst. Commun. 10 217
[13] Chambers J E, Murision M A 2000 Astron. J. 119 425
[14] Suzuki M 1995 Phys. Lett. A 201 425
[15] Chin S A 1997 Phys. Lett. A 75 226
[16] Chin S A, Chen C R 2001 J. Chem. Phys. 114 7338
[17] Chin S A, Chen C R 2005 Celest. Mech. Dyn. Astron. 91 301
[18] Chin S A, Anisimov P 2006 J. Chem. Phys. 124 054106
[19] Chin S A 2007 Phys. Rev. E 75 036701
[20] Omelyan I P, Mryglod I M, Folk R 2003 Comput. Phys. Commun. 151 272
[21] Omelyan I P, Mryglod I M, Folk R 2002 Phys. Rev. E 66 026701
[22] Xu J, Wu X 2010 Res. Astron. Astrophys. 10 173
[23] McLachlan R I, Atela P 1992 Nonlinearity 5 541
[24] Li R, Wu X 2010 Sci. China G 53 1600
[25] Casas F, Murua A 2009 J. Math. Phys. 50 033513
[26] Blanes S, Casas F, Murua A 2008 arXiv: 0812. 0377
[27] Wu X, Huang T Y, Zhang H 2006 Phys. Rev. D 74 083001
[28] Wu X, Xie Y 2007 Phys. Rev. D 76 124004
[29] Wu X, Xie Y 2008 Phys. Rev. D 77 103012
[30] Zhu J F, Wu X, Ma D Z 2007 Chin. J. Astron. Astrophys. 7 601
[31] Han W B 2008 Gen. Relat. Gravit. 40 1831
[32] Zhao H J, Du M L 2007 Acta Phys. Sin. 56 3827 (in Chinese)
[33] Mikkola S 1997 Celest. Mech. Dyn. Astron. 67 145
[34] Tselios K, Simos T E 2003 J. Math. Chem. 34 83
[35] Liu X S, Ding P Z 2004 Prog. Phys. 24 47 (in Chinese) [刘学深、 丁培柱 2004 物理学进展 24 47]
[36] Liu X S, Zhou Z Y, Ding P Z, Pan S F 2000 Int. J. Quant. Chem. 79 343
[37] Quarteroni A, Sacco R, Saleri F 2000 Numerical Mathematics (Berlin: Springer Science) p254
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[1] Feng K 1986 J. Comput. Math. 4 279
[2] [赵海军、 杜孟利 2007 56 3827]
[3] Ruth R D 1983 IEEE Trans. Nucl. Sci. NS-30 2669
[4] Chi Y H, Liu X S, Ding P Z 2006 Acta Phys. Sin. 55 6320 (in Chinese) [匙玉华、 刘学深、 丁培柱 2006 55 6320]
[5] Luo X Y, Liu X S, Ding P Z 2007 Acta Phys. Sin. 56 604 (in Chinese)[罗香怡、 刘学深、 丁培柱 2007 56 604]
[6] Liu X S, Wei J Y, Ding P Z 2005 Chin. Phys. 14 231
[7] Bian X B, Qiao H X, Shi T Y 2007 Chin. Phys. 16 1822
[8] Hu W P, Deng Z C 2008 Chin. Phys. B 17 3923
[9] Forest E, Ruth R D 1990 Physica D 43 105
[10] Yoshida H 1990 Phys. Lett. A 150 262
[11] Wisdom J, Holman M 1991 Astron. J. 102 1528
[12] Wisdom J, Holman M, Touma J 1996 Fields Inst. Commun. 10 217
[13] Chambers J E, Murision M A 2000 Astron. J. 119 425
[14] Suzuki M 1995 Phys. Lett. A 201 425
[15] Chin S A 1997 Phys. Lett. A 75 226
[16] Chin S A, Chen C R 2001 J. Chem. Phys. 114 7338
[17] Chin S A, Chen C R 2005 Celest. Mech. Dyn. Astron. 91 301
[18] Chin S A, Anisimov P 2006 J. Chem. Phys. 124 054106
[19] Chin S A 2007 Phys. Rev. E 75 036701
[20] Omelyan I P, Mryglod I M, Folk R 2003 Comput. Phys. Commun. 151 272
[21] Omelyan I P, Mryglod I M, Folk R 2002 Phys. Rev. E 66 026701
[22] Xu J, Wu X 2010 Res. Astron. Astrophys. 10 173
[23] McLachlan R I, Atela P 1992 Nonlinearity 5 541
[24] Li R, Wu X 2010 Sci. China G 53 1600
[25] Casas F, Murua A 2009 J. Math. Phys. 50 033513
[26] Blanes S, Casas F, Murua A 2008 arXiv: 0812. 0377
[27] Wu X, Huang T Y, Zhang H 2006 Phys. Rev. D 74 083001
[28] Wu X, Xie Y 2007 Phys. Rev. D 76 124004
[29] Wu X, Xie Y 2008 Phys. Rev. D 77 103012
[30] Zhu J F, Wu X, Ma D Z 2007 Chin. J. Astron. Astrophys. 7 601
[31] Han W B 2008 Gen. Relat. Gravit. 40 1831
[32] Zhao H J, Du M L 2007 Acta Phys. Sin. 56 3827 (in Chinese)
[33] Mikkola S 1997 Celest. Mech. Dyn. Astron. 67 145
[34] Tselios K, Simos T E 2003 J. Math. Chem. 34 83
[35] Liu X S, Ding P Z 2004 Prog. Phys. 24 47 (in Chinese) [刘学深、 丁培柱 2004 物理学进展 24 47]
[36] Liu X S, Zhou Z Y, Ding P Z, Pan S F 2000 Int. J. Quant. Chem. 79 343
[37] Quarteroni A, Sacco R, Saleri F 2000 Numerical Mathematics (Berlin: Springer Science) p254
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