|
|
|
A local energy-preserving scheme for Klein–Gordon–Schrödinger equations |
| Cai Jia-Xiang (蔡加祥)a b, Wang Jia-Lin (汪佳玲)a, Wang Yu-Shun (王雨顺)a |
a Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, China;
b School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China |
|
|
|
|
Abstract A local energy conservation law is proposed for the Klein–Gordon–Schrödinger equations, which is held in any local time–space region. The local property is independent of the boundary condition and more essential than the global energy conservation law. To develop a numerical method preserving the intrinsic properties as much as possible, we propose a local energy-preserving (LEP) scheme for the equations. The merit of the proposed scheme is that the local energy conservation law can hold exactly in any time–space region. With the periodic boundary conditions, the scheme also possesses the discrete change and global energy conservation laws. A nonlinear analysis shows that the LEP scheme converges to the exact solutions with order O(τ2+h2). The theoretical properties are verified by numerical experiments.
|
Received: 28 November 2014
Revised: 09 December 2014
Accepted manuscript online:
|
|
PACS:
|
02.60.Cb
|
(Numerical simulation; solution of equations)
|
| |
02.70.Bf
|
(Finite-difference methods)
|
| |
02.60.Lj
|
(Ordinary and partial differential equations; boundary value problems)
|
|
| Fund: Project of Graduate Education Innovation of Jiangsu Province, China (Grant No. CXLX13_366). |
Corresponding Authors:
Wang Yu-Shun
E-mail: thomasjeer@sohu.com, wangyushun@njnu.edu.cn
|
| About author: 02.60.Cb; 02.70.Bf; 02.60.Lj |
Cite this article:
Cai Jia-Xiang (蔡加祥), Wang Jia-Lin (汪佳玲), Wang Yu-Shun (王雨顺) A local energy-preserving scheme for Klein–Gordon–Schrödinger equations 2015 Chin. Phys. B 24 050205
|
| [1] |
Fukuda I and Tsutsumi H 1975 Proc. Japan Acad. 51 402
|
| [2] |
Lu K and Wang B 2001 J. Differ. equations 170 281
|
| [3] |
Natali F and Pastor A 2010 Commun. Pure Appl. Anal. 9 413
|
| [4] |
Zhang L 2005 Appl. Math. Comput. 163 343
|
| [5] |
Kong L, Liu R and Xu Z 2006 Appl. Math. Comput. 181 342
|
| [6] |
Cai J, Yang B and Liang H 2013 Chin. Phys. B 22 030209
|
| [7] |
Hong J, Jiang S and Li C 2009 J. Comput. Phys. 228 3517
|
| [8] |
Kong L 2010 Comput. Phys. Commun. 181 1369
|
| [9] |
Hong J 2007 J. Phys. A: Math. Theor. 40 9125
|
| [10] |
Wang T and Jiang Y 2012 Commun. Nonlinear Sci. Numer. Simul. 17 4565
|
| [11] |
Xiang X 1988 J. Comput. Appl. Math. 21 161
|
| [12] |
Bao W and Yang L 2007 J. Comput. Phys. 225 1863
|
| [13] |
Zhang H 2014 Chin. Phys. B 23 080204
|
| [14] |
Xanthopoulos P and Zouraris G 2008 Discrete Contin. Dyn. Syst. Ser. B 10 239
|
| [15] |
Qin M Z and Wang Y S 2012 (Zhejiang: Science and Technology Publishing House)
|
| [16] |
Wang Y, Wang B and Qin M 2008 Sci. Chin. Series A: Mathematics 51 2115
|
| [17] |
Cai J, Wang Y and Liang H 2013 J. Comput. Phys. 239 30
|
| [18] |
Cai J and Wang Y 2013 J. Comput. Phys. 239 72
|
| [19] |
Zhou Y 1990 (Beijing: International Academic Publishers)
|
| No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|
