| GENERAL |
|
|
|
|
A New Class of Scaling Correction Methods |
| MEI Li-Jie1,WU Xin1**,LIU Fu-Yao2 |
1School of Science, Nanchang University, Nanchang 330031
2Department of Applied Mathematics, Shanghai Lixin University of Commerce, Shanghai 201600 |
|
| Cite this article: |
|
MEI Li-Jie, WU Xin**, LIU Fu-Yao 2012 Chin. Phys. Lett. 29 050201 |
|
|
|
|
Abstract When conventional integrators like Runge–Kutta-type algorithms are used, numerical errors can make an orbit deviate from a hypersurface determined by many constraints, which leads to unreliable numerical solutions. Scaling correction methods are a powerful tool to avoid this. We focus on their applications, and also develop a family of new velocity multiple scaling correction methods where scale factors only act on the related components of the integrated momenta. They can preserve exactly some first integrals of motion in discrete or continuous dynamical systems, so that rapid growth of roundoff or truncation errors is suppressed significantly.
|
| Keywords:
02.70.-c
05.10.-a
45.10.-b
|
|
|
Received: 19 July 2011
Published: 30 April 2012
|
|
| 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)
|
|
|
|
|
|
[1] Feng K and Qin M Z 2010 Symplectic Geometric Algorithms for Hamiltonian Systems 1st edn (Berlin: Springer)[2] Zhong S Y, Wu X, Liu S Q and Deng X F 2010 Phys. Rev. D 82 124040[3] Li R and Wu X 2011 Chin. Phys. Lett. 28 070201[4] Li R and Wu X 2010 Sci. Chin. Phys. Mech. Astron. 53 1600[5] Li R and Wu X 2010 Acta. Phys. Sin. 59 7135 (in Chinese)[6] Sun W, Wu X and Huang G Q 2011 Res. Astron. Astrophys. 11 353[7] Xu J and Wu X 2010 Res. Astron. Astrophys. 10 173[8] Nacozy P E 1971 Astrophys. Space Sci. 14 40[9] Baumgarte J 1972 Celest. Mech. 4 490[10] Murrson M A 1989 Astron. J. 97 1496[11] Zhsng K 1996 Comput. Phys. Commun. 99 53[12] Wu X, Zhu J F, He J Z and Zhang H 2006 Comput. Phys. Commun. 175 15[13] Wu X and He J Z 2006 Int. J. Mod. Phys. C 17 1613[14] Wu X, Huang T Y, Wan X S and Zhang H 2007 Astron. J. 133 2643[15] Han W B and Liao X H 2007 Comput. Phys. Commun. 177 500[16] Ma D Z, Wu X and Zhong S Y 2008 Astrophys. J. 687 1294[17] Ma D Z, Wu X and Liu F Y 2008 Int. J. Mod. Phys. C 19 1411[18] Zhong S Y and Wu X 2009 Astrophys. Space Sci. 324 31[19] Liu L and Liao X H 1994 Celest. Mech. Dyn. Astron. 59 221[20] Fukushima T 2003 Astron. J. 126 1097[21] Fukushima T 2003 Astron. J. 126 2567[22] Ma D Z, Wu X and Zhu J F 2008 New Astron. 13 216[23] Zhong S Y and Wu X 2010 Phys. Rev. D 81 104037[24] Aizawa Y and Saito N 1972 J. Phys. Soc. Jpn. 32 1636 |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
