GENERAL |
|
|
|
|
Application of the St?rmer–Verlet-Like Symplectic Method to the Wave Equation* |
QIU Yu-Fen, WU Xin** |
School of Science, Nanchang University, Nanchang 330031
|
|
Cite this article: |
QIU Yu-Fen, WU Xin 2013 Chin. Phys. Lett. 30 080203 |
|
|
Abstract A fourth-order three-stage symplectic integrator similar to the second-order St?rmer–Verlet method has been proposed and used before [Chin. Phys. Lett. 28 (2011) 070201; Eur. Phys. J. Plus 126 (2011) 73]. Continuing the work initiated in the publications, we investigate the numerical performance of the integrator applied to a one-dimensional wave equation, which is expressed as a discrete Hamiltonian system with a fourth-order central difference approximation to a second-order partial derivative with respect to the space variable. It is shown that the St?rmer–Verlet-like scheme has a larger numerical stable zone than either the St?rmer–Verlet method or the fourth-order Forest–Ruth symplectic algorithm, and its numerical errors in the discrete Hamiltonian and numerical solution are also smaller.
|
|
Received: 08 May 2013
Published: 21 November 2013
|
|
PACS: |
02.70.-c
|
(Computational techniques; simulations)
|
|
02.60.-x
|
(Numerical approximation and analysis)
|
|
45.10.-b
|
(Computational methods in classical mechanics)
|
|
|
|
|
[1] Hairer E, Lubich C and Wanner G 1999 Geometric Numerical Integration (Berlin: Springer) [2] Feng K and Qin M Z 2009 Symplectic Geometric Algorithms for Hamiltonian Systems (Hangzhou: Zhejiang Science and Technology Publishing House) [3] Ma D Z, Wu X and Zhong S Y 2008 Astrophys. J. 687 1294 [4] Zhong S Y and Wu X 2010 Phys. Rev. D 81 104037 [5] Mei L J, Wu X and Liu F Y 2012 Chin. Phys. Lett. 29 050201 [6] Zhong S Y, Wu X, Liu S Q and Deng X F 2010 Phys. Rev. D 82 124040 [7] Zhong S Y and Wu X 2011 Acta Phys. Sin. 60 090402 (in Chinese) [8] Mei L, Wu X and Liu F 2013 Eur. Phys. J. C 73 2413 [9] Yoshida H 1990 Phys. Lett. A 150 262 [10] Forest E and Ruth R D 1990 Physica D 43 105 [11] Mei L J, Wu X and Liu F Y 2013 Eur. Phys. J. C 73 2413 [12] Ruth R D 1983 IEEE Trans. Nucl. Sci. 30 2669 [13] Chin S A 2007 Phys. Rev. E 75 036701 [14] Xu J and Wu X 2010 Res. Astron. Astrophys. 10 173 [15] Sun W, Wu X and Huang G Q 2011 Res. Astron. Astrophys. 11 353 [16] Li R and Wu X 2010 Sci. Chin. Phys. Mech. Astron. 53 1600 [17] Li R and Wu X 2010 Acta Phys. Sin. 59 7135 (in Chinese) [18] Chen Y L and Wu X 2013 Acta Phys. Sin. 62 140501 (in Chinese) [19] Li R and Wu X 2011 Chin. Phys. Lett. 28 070201 [20] Li R and Wu X 2011 Eur. Phys. J. Plus 126 73 [21] Qin M Z and Zhang M Q 1990 Comput. Math. Appl. 19 51 [22] Boreux J, Carletti T and Hubaux C 2010 arXiv:1012.3242 [nlin.PS] [23] Chin S A 2012 arXiv:1206.1743 [math.NA] [24] Hu W, Deng Z, Han S and Zhang W 2013 J. Comput. Phys. 235 394 [25] Lichtenberg A J and Lieberman M A 1983 Regular and Chaotic Dynamics (Berlin: Springer-Verlag) |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|