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立方Schrödinger方程的半隐格式BDF2-FEM无条件最优误差估计

代猛 尹小艳

代猛, 尹小艳. 立方Schrödinger方程的半隐格式BDF2-FEM无条件最优误差估计[J]. 应用数学和力学, 2019, 40(6): 663-681. doi: 10.21656/1000-0887.390209
引用本文: 代猛, 尹小艳. 立方Schrödinger方程的半隐格式BDF2-FEM无条件最优误差估计[J]. 应用数学和力学, 2019, 40(6): 663-681. doi: 10.21656/1000-0887.390209
DAI Meng, YIN Xiaoyan. Unconditionally Optimal Error Estimates of the Semi-Implicit BDF2-FEM for Cubic Schrödinger Equations[J]. Applied Mathematics and Mechanics, 2019, 40(6): 663-681. doi: 10.21656/1000-0887.390209
Citation: DAI Meng, YIN Xiaoyan. Unconditionally Optimal Error Estimates of the Semi-Implicit BDF2-FEM for Cubic Schrödinger Equations[J]. Applied Mathematics and Mechanics, 2019, 40(6): 663-681. doi: 10.21656/1000-0887.390209

立方Schrödinger方程的半隐格式BDF2-FEM无条件最优误差估计

doi: 10.21656/1000-0887.390209
基金项目: 国家自然科学基金(面上项目)(11771259);中央高校基础科研业务费(JB180714)
详细信息
    作者简介:

    代猛(1993—), 男, 硕士生(E-mail: dm1614720343@163.com);尹小艳(1979—), 女, 副教授, 博士, 硕士生导师(通讯作者. E-mail: xyyin@mail.xidian.edu.cn).

  • 中图分类号: O241.82

Unconditionally Optimal Error Estimates of the Semi-Implicit BDF2-FEM for Cubic Schrödinger Equations

Funds: The National Natural Science Foundation of China(General Program)(11771259)
  • 摘要: 研究了立方Schrödinger方程的二阶向后差分有限元方法(BDF2-FEM)的无条件最优误差估计.首先,将误差分为时间误差和空间误差两部分.通过引入时间离散方程,得到时间离散方程解的一致有界性,并给出时间误差估计.从而得到该方程在半隐格式下BDF2FEM无条件最优误差估计.最后,用数值算例验证了理论分析.
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出版历程
  • 收稿日期:  2018-07-31
  • 修回日期:  2019-04-13
  • 刊出日期:  2019-06-01

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