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一类非线性Schrodinger方程的守恒差分法与Fourier谱方法
  • ISSN号：1006-6837
  • 期刊名称：《数学研究》
  • 时间：0
  • 分类：O241.82[理学—计算数学;理学—数学]
  • 作者机构：[1]厦门大学数学科学学院,福建厦门361005
  • 相关基金：国家自然科学基金重点项目（10531080）;教育部优秀青年教师资助计划项目;973高性能科学计算项目（2005CB321703）
作者： 龚玉飞[1], 许传炬[1]
关键词： Schrgdinger方程, 差分格式, FOURIER谱方法, 能量守恒, 收敛性, Schrodinger equation, Finite difference scheme, Fourier-spectral method, Energy conservations , Convergence
中文摘要：

考察了一类带导数项的非线性Schrodinger方程的周期边值问题，提出了一种守恒的差分格式，在空间方向上采用Fourier谱方法，证明了格式的稳定性和收敛性．数值试验得到了与理论分析一致的结果．

英文摘要：

In this paper, a conservative finite difference scheme in time and Fourier spectral method in space is proposed for the Schrodinger equation involving the nonlinear derivative term with periodic boundary conditions, and the convergence and stability of the proposed scheme are proved. A series of numerical experiments are performed to support the theoretical claim.

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期刊信息
  • 《数学研究》
  • 主管单位:厦门大学
  • 主办单位:厦门大学数学科学学院 福建省数学会
  • 主编：林群
  • 地址：厦门大学数学系
  • 邮编：361005
  • 邮箱：jmaths@xmu.edu.cn
  • 电话：0592-2580752 21828321
  • 国际标准刊号：ISSN：1006-6837
  • 国内统一刊号：ISSN：35-1177/O1
  • 邮发代号:
  • 获奖情况:
  • 国内外数据库收录:
  • 美国数学评论（网络版）,德国数学文摘
  • 被引量:1284