求解时间分布阶扩散方程的两个高阶有限差分格式

胡嘉卉; 王俊刚; 聂玉峰

doi:10.21656/1000-0887.390358

求解时间分布阶扩散方程的两个高阶有限差分格式

doi: 10.21656/1000-0887.390358

¹西北工业大学应用数学系, 西安 710129;²河南工业大学理学院, 郑州 450001

基金项目: 国家自然科学基金（11471262）

详细信息

作者简介:
胡嘉卉（1980—），女，博士生(E-mail: hujh@mail.nwpu.edu.cn);聂玉峰(1968—)，男，教授，博士生导师(通讯作者. E-mail: yfnie@nwpu.edu.cn).

中图分类号: O242.2
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出版历程
- 收稿日期: 2018-12-25
- 修回日期: 2019-03-09
- 刊出日期: 2019-07-01

Two High-Order Difference Schemes for Solving Time Distributed-Order Diffusion Equations

¹Department of Applied Mathematics, Northwestern Polytechnical University,Xi’an 710129, P.R.China;²School of Sciences, Henan University of Technology, Zhengzhou 450001, P.R.China

Funds: The National Natural Science Foundation of China(11471262)

摘要

摘要: 基于复化Simpson公式和复化两点Gauss-Legendre公式，构造了两个求解时间分布阶扩散方程的高阶有限差分格式.不同于以往文献中提出的时间一阶或二阶格式，这两种格式在时间方向都具有三阶精度，而在分布阶和空间方向可达到四阶精度.数值结果表明，两种算法都是稳定且收敛的，从而是有效的.两种格式的收敛速率也通过数值实验进行了验证，并且通过和文献中的算法对比可以得出其更为高效,
- 时间分布阶扩散方程 /
- 分数阶导数 /
- 高阶差分格式 /
- 收敛速率
Abstract: Based on the composite Simpson’s quadrature rule and the composite 2-point Gauss-Legendre quadrature rule, 2 high-order finite difference schemes were proposed for solving time distributed-order diffusion equations. Other than the existing methods whose convergence rates are only 1st-order or 2nd-order in the temporal domain, the proposed 2 schemes both have 3rd-order convergence rates in the temporal domain, and 4th-order rates in the spatial domain and the distributed order, respectively. Such high-order convergence rates were further verified with numerical examples. The results show that, both of the proposed 2 schemes are stable, and have higher accuracy and efficiency compared with existing algorithms.
- time distributed-order diffusion equation /
- fractional derivative /
- high-order difference scheme /
- convergence rate

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参考文献(18)

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求解时间分布阶扩散方程的两个高阶有限差分格式

doi: 10.21656/1000-0887.390358

作者简介:
胡嘉卉（1980—），女，博士生(E-mail: hujh@mail.nwpu.edu.cn);聂玉峰(1968—)，男，教授，博士生导师(通讯作者. E-mail: yfnie@nwpu.edu.cn).

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Two High-Order Difference Schemes for Solving Time Distributed-Order Diffusion Equations

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留言板

求解时间分布阶扩散方程的两个高阶有限差分格式

doi: 10.21656/1000-0887.390358

作者简介: 胡嘉卉（1980—），女，博士生(E-mail: hujh@mail.nwpu.edu.cn);聂玉峰(1968—)，男，教授，博士生导师(通讯作者. E-mail: yfnie@nwpu.edu.cn).

计量

出版历程

Two High-Order Difference Schemes for Solving Time Distributed-Order Diffusion Equations

计量

出版历程

目录

作者简介:
胡嘉卉（1980—），女，博士生(E-mail: hujh@mail.nwpu.edu.cn);聂玉峰(1968—)，男，教授，博士生导师(通讯作者. E-mail: yfnie@nwpu.edu.cn).