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一类分数阶Langevin方程block-by-block算法的数值分析

张嫚 曹艳华 杨晓忠

张嫚, 曹艳华, 杨晓忠. 一类分数阶Langevin方程block-by-block算法的数值分析[J]. 应用数学和力学, 2021, 42(6): 562-574. doi: 10.21656/1000-0887.410337
引用本文: 张嫚, 曹艳华, 杨晓忠. 一类分数阶Langevin方程block-by-block算法的数值分析[J]. 应用数学和力学, 2021, 42(6): 562-574. doi: 10.21656/1000-0887.410337
ZHANG Man, CAO Yanhua, YANG Xiaozhong. Numerical Analysis of a Class of Fractional Langevin Equations With the Block-by-Block Method[J]. Applied Mathematics and Mechanics, 2021, 42(6): 562-574. doi: 10.21656/1000-0887.410337
Citation: ZHANG Man, CAO Yanhua, YANG Xiaozhong. Numerical Analysis of a Class of Fractional Langevin Equations With the Block-by-Block Method[J]. Applied Mathematics and Mechanics, 2021, 42(6): 562-574. doi: 10.21656/1000-0887.410337

一类分数阶Langevin方程block-by-block算法的数值分析

doi: 10.21656/1000-0887.410337
基金项目: 

国家科技重大专项子课题(2017ZX07101001-01)

详细信息
    作者简介:

    张嫚(1995—),女,硕士生(E-mail: zhangman82@163.com);杨晓忠(1965—),男,教授,博士生导师(通讯作者. E-mail: yxiaozh@ncepu.edu.cn).

    通讯作者:

    杨晓忠(1965—),男,教授,博士生导师(通讯作者. E-mail: yxiaozh@ncepu.edu.cn).

  • 中图分类号: O211.63

Numerical Analysis of a Class of Fractional Langevin Equations With the Block-by-Block Method

  • 摘要: 分数阶Langevin方程有重要的科学意义和工程应用价值,基于经典block-by-block算法,求解了一类含有Caputo导数的分数阶Langevin方程的数值解.Block-by-block算法通过引入二次Lagrange基函数插值,构造出逐块收敛的非线性方程组,通过在每一块耦合求得分数阶Langevin方程的数值解.在0<α<1条件下,应用随机Taylor展开证明block-by-block算法是3+α阶收敛的,数值试验表明在不同α和时间步长h取值下,block-by-block算法具有稳定性和收敛性,克服了现有方法求解分数阶Langevin方程速度慢精度低的缺点,表明block-by-block算法求解分数阶Langevin方程是高效的.
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出版历程
  • 收稿日期:  2020-10-29
  • 修回日期:  2020-11-21

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