›› 2014, Vol. 23 ›› Issue (12): 120203-120203.doi: 10.1088/1674-1056/23/12/120203

• GENERAL • 上一篇    下一篇

A conservative Fourier pseudospectral algorithm for the nonlinear Schrödinger equation

吕忠全a b c, 张鲁明a, 王雨顺c   

  1. 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
  • 收稿日期:2014-04-21 修回日期:2014-08-18 出版日期:2014-12-15 发布日期:2014-12-15
  • 基金资助:
    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).

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   

  1. 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
  • Received:2014-04-21 Revised:2014-08-18 Online:2014-12-15 Published:2014-12-15
  • Contact: Lv Zhong-Quan E-mail:zhqlv@njfu.edu.cn
  • Supported by:
    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).

PDF (PC)

415

赞

摘要： 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.

关键词: Fourier pseudospectral method, Schrö, dinger equation, conservation law, convergence

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.

Key words: Fourier pseudospectral method, Schrödinger equation, conservation law, convergence

中图分类号:  (Numerical simulation; solution of equations)

  • 02.60.Cb
02.70.Bf (Finite-difference methods) 02.70.Jn (Collocation methods) 02.70.Hm (Spectral methods)