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

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

华北电力大学数理学院信息与计算研究所，北京 102206

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
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- 文章访问数: 803
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- PDF下载量: 82
- 被引次数: 0
出版历程
- 收稿日期: 2020-10-29
- 修回日期: 2020-11-21

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

Institute of Information and Computation, School of Mathematics and Physics, North China Electric Power University, Beijing 102206, P.R.China

摘要

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.
- 分数阶Langevin方程 /
- block-by-block算法 /
- 稳定性 /
- 收敛性 /
- 数值试验
Abstract: The fractional Langevin equation is of great scientific significance and engineering application value. Based on the classical block-by-block method, the numerical solution of a class of fractional Langevin equations with Caputo derivatives was obtained. Through introduction of the quadratic Lagrange basis function interpolation, the block-by-block convergent nonlinear equations were constructed, and the numerical solution of the Langevin equation was obtained by coupling in each block. Under the condition of 0<α<1, the stochastic Taylor expansion was used to prove that the block-by-block method is (3+α)-order convergent. Numerical experiments show that, the block-by-block method is stable and convergent under different values of α and time step h,and overcomes the existing methods’ disadvantages of slow speed and poor accuracy for solving fractional Langevin equations.
- fractional Langevin equation /
- block-by-block method /
- stability /
- convergence /
- numerical experiment

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参考文献(25)

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一类分数阶Langevin方程block-by-block算法的数值分析

doi: 10.21656/1000-0887.410337

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).

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

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目录

留言板

一类分数阶Langevin方程block-by-block算法的数值分析

doi: 10.21656/1000-0887.410337

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).

计量

出版历程

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

计量

出版历程

目录

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).