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 引用本文: 胡嘉卉, 王俊刚, 聂玉峰. 求解时间分布阶扩散方程的两个高阶有限差分格式[J]. 应用数学和力学, 2019, 40(7): 791-800.
HU Jiahui, WANG Jungang, NIE Yufeng. Two High-Order Difference Schemes for Solving Time Distributed-Order Diffusion Equations[J]. Applied Mathematics and Mechanics, 2019, 40(7): 791-800. doi: 10.21656/1000-0887.390358
 Citation: HU Jiahui, WANG Jungang, NIE Yufeng. Two High-Order Difference Schemes for Solving Time Distributed-Order Diffusion Equations[J]. Applied Mathematics and Mechanics, 2019, 40(7): 791-800.

## 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).
• 中图分类号: O242.2

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

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

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