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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.
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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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