A conservative Fourier pseudospectral algorithm for the nonlinear Schrodinger equation  被引量:1

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作  者:吕忠全 张鲁明 王雨顺 

机构地区:[1]College of Science,Nanjing University of Aeronautics and Astronautics [2]College of Science,Nanjing Forestry University [3]School of Mathematical Sciences,Nanjing Normal University

出  处:《Chinese Physics B》2014年第12期21-29,共9页中国物理B(英文版)

基  金: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);the Fund Project for Highly Educated Talents of Nanjing Forestry University(Grant No.GXL201320)

摘  要:In this paper, we derive a new method for a nonlinear Schrodinger 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.In this paper, we derive a new method for a nonlinear Schrodinger 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 Schrdinger equation conservation law CONVERGENCE 

分 类 号:O175[理学—数学]

 

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