四阶分数阶扩散波动方程的两网格混合元快速算法

doi:10.12286/jssx.j2021-0775

计算数学 ›› 2022, Vol. 44 ›› Issue (4): 496-507.DOI: 10.12286/jssx.j2021-0775

四阶分数阶扩散波动方程的两网格混合元快速算法

王金凤¹, 尹保利², 刘洋², 李宏²

1. 内蒙古财经大学统计与数学学院, 呼和浩特 010070;
2. 内蒙古大学数学科学学院, 呼和浩特 010021

收稿日期:2021-01-29 出版日期:2022-11-14 发布日期:2022-11-08
通讯作者: 刘洋,Email:mathliuyang@imu.edu.cn.
基金资助:
国家自然科学基金项目（12061053，12161063），内蒙古自然科学基金项目（2021MS01018，2022LHMS01004），内蒙古自治区高校创新团队项目（NMGIRT2207），“草原英才”工程青年创新创业人才项目资助.

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王金凤, 尹保利, 刘洋, 李宏. 四阶分数阶扩散波动方程的两网格混合元快速算法[J]. 计算数学, 2022, 44(4): 496-507.

Wang Jinfeng, Yin Baoli, Liu Yang, Li Hong. A FAST TWO-GRID MIXED ELEMENT METHOD FOR A FOURTH-ORDER FRACTIONAL DIFFUSION-WAVE EQUATION[J]. Mathematica Numerica Sinica, 2022, 44(4): 496-507.

A FAST TWO-GRID MIXED ELEMENT METHOD FOR A FOURTH-ORDER FRACTIONAL DIFFUSION-WAVE EQUATION

Wang Jinfeng¹, Yin Baoli², Liu Yang², Li Hong²

1. School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, China;
2. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China

Received:2021-01-29 Online:2022-11-14 Published:2022-11-08

本文研究四阶分数阶扩散波动方程模型的基于新混合元方法的快速两网格算法.讨论该方法的稳定性,推导三个未知函数的$L^2$模意义下的最优误差估计.最后通过数值例子验证两网格混合元算法的高效性和理论结果的正确性.

关键词： 四阶时间分数阶扩散波动方程, 修正$L1$公式, 两网格算法, 混合元方法, 误差估计

In this paper, a two-grid mixed element algorithm is proposed to solve a fourth-order fractional diffusion-wave model. The stability of the studied two-grid mixed element algorithm is proven, and the optimal a priori error estimates in L²-norm for three unknown functions are derived. Finally, the numerical results are calculated to verify the efficiency of the algorithm and the correctness of the theory results.

Key words: fourth-order time fractional diffusion-wave equation, modified L1-formula, two-grid algorithm, mixed element method, error estimates

MR(2010)主题分类:

65N15
65N30

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摘要

四阶分数阶扩散波动方程的两网格混合元快速算法

A FAST TWO-GRID MIXED ELEMENT METHOD FOR A FOURTH-ORDER FRACTIONAL DIFFUSION-WAVE EQUATION

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