Chin. Phys. Lett.  2008, Vol. 25 Issue (5): 1538-1540    DOI:
Original Articles |
Two New Simple Multi-Symplectic Schemes for the Nonlinear Schrodinger Equation
WANG Yu-Shun1;LI Qing-Hong2; SONG Yong-Zhong1
1School of Mathematics and Computer Sciences, Nanjing Normal University, Nanjing 2100972Department of Mathematics, Chuzhou University, Chuzhou 239000
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WANG Yu-Shun, LI Qing-Hong, SONG Yong-Zhong 2008 Chin. Phys. Lett. 25 1538-1540
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Abstract We investigate the multi-symplectic Euler-box scheme for the nonlinear Schrodinger equation. Two new simple semi-explicit scheme are derived. A composition scheme based on the new derived schemes is also discussed. Some numerical results are reported to illustrate the efficiency of the new
schemes.
Keywords: 20.60.Cb      02.70.Bf      45.10.Na      45.20.Dh     
Received: 14 August 2007      Published: 29 April 2008
PACS:  20.60.Cb  
  02.70.Bf (Finite-difference methods)  
  45.10.Na (Geometrical and tensorial methods)  
  45.20.dh (Energy conservation)  
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https://cpl.iphy.ac.cn/       OR      https://cpl.iphy.ac.cn/Y2008/V25/I5/01538
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WANG Yu-Shun
LI Qing-Hong
SONG Yong-Zhong
[1] Tang Y F, Cao J W, Liu X T and Sun Y C 2007 J. Phys.A: Math. Theor. 40 2425
[2] Liu X S, Qi Y Y, He J F and Ding P Z 2007 Commun.Comput. Phys. 2 1
[3] Bridge T J and Reich S 2001 Phys. Lett. A 284 184
[4] Chen J B 2001 Appl. Math. Comput. 124 371
[5] Hong J L, Liu Y, Munthe-Kaas H and Zanna A 2006 Appl.Numer. Math. 56 814
[6] Moore B and Reich S 2003 Numer. Math. 95 625
[7] Chen J B and Qin M Z 2003 J. Comput. Math. 21647
[8] Wang Y S and Wang B 2005 Appl. Math. Comput. 166 608
[9] Yashida H 1990 Phys. Lett. A 150 262
[10] Qin M Z and Zhu W J 1992 Computing 17 309
[11] Hairer E, Lubich C and Wanner G 2002 GeometricNumerical Integration, Structure-Preserving Algorithms forOrdinary Differential Equations (Berlin: Springer)
[12] Chen J B 2005 Appl. Math. Comp. 170 1394
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