|
|
A conservative Fourier pseudospectral algorithm for the nonlinear Schrödinger equation |
Lv Zhong-Quan (吕忠全)a b c, Zhang Lu-Ming (张鲁明)a, Wang Yu-Shun (王雨顺)c |
a College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China; b College of Science, Nanjing Forestry University, Nanjing 210037, China; c School of Mathematical Sciences, Nanjing Normal University, Nanjing 210097, China |
|
|
Abstract In this paper, we derive a new method for a nonlinear Schrödinger system by using the square of the first-order Fourier spectral differentiation matrix D1 instead of the traditional second-order Fourier spectral differentiation matrix D2 to approximate the second derivative. We prove that the proposed method preserves the charge and energy conservation laws exactly. A deduction argument is used to prove that the numerical solution is second-order convergent to the exact solutions in ‖·‖2 norm. Some numerical results are reported to illustrate the efficiency of the new scheme in preserving the charge and energy conservation laws.
|
Received: 21 April 2014
Revised: 18 August 2014
Accepted manuscript online:
|
PACS:
|
02.60.Cb
|
(Numerical simulation; solution of equations)
|
|
02.70.Bf
|
(Finite-difference methods)
|
|
02.70.Jn
|
(Collocation methods)
|
|
02.70.Hm
|
(Spectral methods)
|
|
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11271195, 41231173, and 11201169), the Postdoctoral Foundation of Jiangsu Province of China (Grant No. 1301030B), the Open Fund Project of Jiangsu Key Laboratory for NSLSCS (Grant No. 201301), and the Fund Project for Highly Educated Talents of Nanjing Forestry University (Grant No. GXL201320). |
Corresponding Authors:
Lv Zhong-Quan
E-mail: zhqlv@njfu.edu.cn
|
Cite this article:
Lv Zhong-Quan (吕忠全), Zhang Lu-Ming (张鲁明), Wang Yu-Shun (王雨顺) A conservative Fourier pseudospectral algorithm for the nonlinear Schrödinger equation 2014 Chin. Phys. B 23 120203
|
[1] |
Menyuk C R 1998 J. Opt. Soc. Am. B: Opt. Phys. 5 392
|
[2] |
Wadati M, Izuka T and Hisakado M 1992 J. Phys. Soc. Jpn. 61 2241
|
[3] |
Feng K and Qin M Z 2010 Symplectic Geometric Algorithms for Hamiltonian Systems (Hangzhou: Science and Technology Press) p. 19 (in Chinese)
|
[4] |
Qin M Z and Wang Y S 2011 Structure-Preserving Algorithm for Partial Differential Equation (Hangzhou: Zhejiang Science and Technology Press) p. 420 (in Chinese)
|
[5] |
Cai J X and Wang Y S 2013 Chin. Phys. B 22 060207
|
[6] |
Akrivis G D 1993 IMA. J. Numer. Anal. 13 115
|
[7] |
Lv Z Q, Wang Y S and Song Y Z 2013 Chin. Phys. Lett. 30 030201
|
[8] |
Dehghan M and Taleei A 2010 Comput. Phys. Comm. 181 43
|
[9] |
Chang Q, Jia E and Sun W 1999 J. Comput. Phys. 148 397
|
[10] |
Wang T C and Guo B L 2011 Sci. China: Ser. A Math. 41 207
|
[11] |
Wang Y S, Li Q H and Song Y Z 2008 Chin. Phys. Lett. 25 1538
|
[12] |
Wang Y S and Li S T 2010 Int. J. Comput. Math. 87 775
|
[13] |
Cooley J W and Tukey J W 1965 Math. Comput. 19 297
|
[14] |
Canuto C, Hussani M and Quarteroni A 1988 Spectral Methods in Fluid Dynamics (New York: Springer-Verlag) p. 275
|
[15] |
Canuto C and Quarteroni A 1982 Math. Comput. 38 67
|
[16] |
Zhou Y L 1990 Application of Discrete Functional Analysis to the Diserence Methods (Beijing: International Academic Publishers)
|
[17] |
Chen J B and Qin M Z 2001 Electr. Trans. Numer. Anal. 12 193
|
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
|
|
|