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
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.
收稿日期: 2013-05-08
出版日期: 2013-11-21
:
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)Symplectic Geometric Algorithms for Hamiltonian Systems (Hangzhou: Zhejiang Science and Technology Publishing House)2008 Astrophys. J. 687 1294 2010 Phys. Rev. D 81 104037 2012 Chin. Phys. Lett. 29 050201 2010 Phys. Rev. D 82 124040 Acta Phys. Sin. 60 090402 (in Chinese)2013 Eur. Phys. J. C 73 2413 1990 Phys. Lett. A 150 262 1990 Physica D 43 105 2013 Eur. Phys. J. C 73 2413 1983 IEEE Trans. Nucl. Sci. 30 2669 2007 Phys. Rev. E 75 036701 2010 Res. Astron. Astrophys. 10 173 2011 Res. Astron. Astrophys. 11 353 2010 Sci. Chin. Phys. Mech. Astron. 53 1600 Acta Phys. Sin. 59 7135 (in Chinese)Acta Phys. Sin. 62 140501 (in Chinese)2011 Chin. Phys. Lett. 28 070201 2011 Eur. Phys. J. Plus 126 73 Comput. Math. Appl. 19 512010 arXiv:1012.3242 [nlin.PS] 2012 arXiv:1206.1743 [math.NA] 2013 J. Comput. Phys. 235 394 Regular and Chaotic Dynamics (Berlin: Springer-Verlag)
[1]
.
[2]
.
[3]
.
[4]
.
[5]
.
[6]
WEI Yi-Kun, QIAN Yue-Hong. Reducing Spurious Velocities at the Interfaces of Two-Phase Flows for Lattice Boltzmann Simulations
[7]
MEI Li-Jie,WU Xin**,LIU Fu-Yao. A New Class of Scaling Correction Methods
[8]
LI Rong;WU Xin**
. Two New Fourth-Order Three-Stage Symplectic Integrators
[9]
Mohammad Noh Daud;Gabriel G. Balint-Kurti. A Time-Dependent Wavepacket Method for Photodissociation Dynamics of Triatomic Molecule
[10]
ZHU Meng-Hua;LIU Liang-Gang;XU Ao-Ao;Ma Tao. Automatic Estimation of Peak Regions in Gamma-Ray Spectra Measured by NaI Detector
[11]
FU Jing-Li;FU Hao. A Field Method for Integrating Equations of Motion of Nonlinear Mechanico-Electrical Coupling Dynamical Systems
[12]
LU Wei-Tao;ZHANG Hua;WANG Shun-Jin. Application of Symplectic Algebraic Dynamics Algorithm to Circular Restricted Three-Body Problem
[13]
WANG Jun-Mao; ZHANG Miao;ZHANG Wen-Liang;ZHANG Rui;HAN Jia-Hua. A New Method for Constructing Travelling Wave Solutions to the modified Benjamin--Bona--Mahoney Equation
[14]
YAO Ruo-Xia;LOU Sen-Yue;. A Maple Package to Compute Lie Symmetry Groups and Symmetry Reductions of (1+1)-Dimensional Nonlinear Systems
[15]
BIAN Xue-Bin;LIU Hong-Ping;SHI Ting-Yun. A Time-Dependent Approach to High-Resolution Photoabsorption Spectrum of Rydberg Atoms in Magnetic Fields
2013, Vol. 30 
