A conservative Fourier pseudospectral algorithm for the nonlinear Schrdinger equation

作者：Lv Zhong Quan; Zhang Lu Ming; Wang Yu Shun; College of Science Nanjing University of Aeronautics and Astronautics; College of Science Nanjing Forestry University; School of Mathematical Sciences Nanjing Normal University

来源：Chinese Physics B, 2014, (12): 25-33.

• Fourier pseudospectral method
• Schrdinger equation
• conservation law
• convergence

In this paper, we derive a new method for a nonlinear Schr ¨odinger 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 · 2norm. Some numerical results are reported to illustrate the efficiency of the new scheme in preserving the charge and energy conservation laws.

• 出版日期2014-12-15
• 单位南京林业大学