Conservative method for simulation of a high-order nonlinear Schrödinger equation with a trapped term

doi:10.1088/1674-1056/24/10/100203

中国物理B ›› 2015, Vol. 24 ›› Issue (10): 100203-100203.doi: 10.1088/1674-1056/24/10/100203

Conservative method for simulation of a high-order nonlinear Schrödinger equation with a trapped term

蔡加祥, 柏传志, 秦志林

School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China

收稿日期:2015-05-07 修回日期:2015-06-25 出版日期:2015-10-05 发布日期:2015-10-05
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11201169 and 11271195) and the Qing Lan Project of Jiangsu Province, China.

Conservative method for simulation of a high-order nonlinear Schrödinger equation with a trapped term

Cai Jia-Xiang (蔡加祥), Bai Chuan-Zhi (柏传志), Qin Zhi-Lin (秦志林)

School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China

Received:2015-05-07 Revised:2015-06-25 Online:2015-10-05 Published:2015-10-05
Contact: Cai Jia-Xiang E-mail:thomasjeer@sohu.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11201169 and 11271195) and the Qing Lan Project of Jiangsu Province, China.

摘要/Abstract

摘要： We propose a new scheme for simulation of a high-order nonlinear Schrödinger equation with a trapped term by using the mid-point rule and Fourier pseudospectral method to approximate time and space derivatives, respectively. The method is proved to be both charge- and energy-conserved. Various numerical experiments for the equation in different cases are conducted. From the numerical evidence, we see the present method provides an accurate solution and conserves the discrete charge and energy invariants to machine accuracy which are consistent with the theoretical analysis.

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

Abstract: We propose a new scheme for simulation of a high-order nonlinear Schrödinger equation with a trapped term by using the mid-point rule and Fourier pseudospectral method to approximate time and space derivatives, respectively. The method is proved to be both charge- and energy-conserved. Various numerical experiments for the equation in different cases are conducted. From the numerical evidence, we see the present method provides an accurate solution and conserves the discrete charge and energy invariants to machine accuracy which are consistent with the theoretical analysis.

Key words: Schrödinger equation, Fourier pseudospectral method, conservation law, fast Fourier transform

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)

蔡加祥, 柏传志, 秦志林. Conservative method for simulation of a high-order nonlinear Schrödinger equation with a trapped term[J]. 中国物理B, 2015, 24(10): 100203-100203.

Cai Jia-Xiang (蔡加祥), Bai Chuan-Zhi (柏传志), Qin Zhi-Lin (秦志林). Conservative method for simulation of a high-order nonlinear Schrödinger equation with a trapped term[J]. Chin. Phys. B, 2015, 24(10): 100203-100203.

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Conservative method for simulation of a high-order nonlinear Schrödinger equation with a trapped term

Conservative method for simulation of a high-order nonlinear Schrödinger equation with a trapped term

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