非线性时间分布阶双曲波动方程的广义BDF2-<em>θ</em>有限元方法

侯雅馨; 刘洋; 李宏

doi:10.21656/1000-0887.450013

非线性时间分布阶双曲波动方程的广义BDF2-θ有限元方法

doi: 10.21656/1000-0887.450013

侯雅馨¹,
刘洋^2, ,,
李宏²

1. 内蒙古工业大学理学院数学系，呼和浩特 010051;
2. 内蒙古大学数学科学学院，呼和浩特 010021

基金项目:

NMGIRT2207)

国家自然科学基金(12161063)；内蒙古自治区 “创新团队发展计划” (NMGIRT2413

详细信息

作者简介:
侯雅馨(1991—)，女，讲师，博士(E-mail: houyaxin@imut.edu.cn)；刘洋(1980—)，男，教授，博士，博士生导师(通讯作者. E-mail: mathliuyang@imu.edu.cn)；李宏(1973—)，女，教授，博士，博士生导师(E-mail: smslh@imu.edu.cn).

通讯作者:
刘洋(1980—)，男，教授，博士，博士生导师(通讯作者. E-mail: mathliuyang@imu.edu.cn).

中图分类号: O357.41
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- 文章访问数: 18
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- 被引次数: 0
出版历程
- 收稿日期: 2024-01-17
- 修回日期: 2024-03-25

A Generalized BDF2-θ Finite Element Method for Nonlinear Distributed-Order Time-Fractional Hyperbolic Wave Equations

HOU Yaxin¹,
LIU Yang^{2
, ,},
LI Hong²

1. Department of Mathematics, College of Science, Inner Mongolia University of Technology, Hohhot 010051, P.R.China;
2. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P.R.China

Funds:

The National Science Foundation of China(12161063)

摘要

摘要:
构造了一种基于带有位移参数θ的广义向后差分公式(广义BDF2-θ)的有限元(FE)方法，用于求解非线性时间分布阶双曲波动方程.时间方向由广义BDF2-θ近似进一步得到FE全离散格式.将具有高阶时间导数的模型转化为包括两个低阶方程的耦合系统.证明了格式的稳定性以及两个函数u和p的最优误差估计结果.最后，通过数值算例验证了格式的可行性和有效性.
- 非线性时间分布阶双曲波动方程 /
- 有限元方法 /
- 广义BDF2-θ /
- 稳定性 /
- 误差估计 /
- 数值模拟
Abstract:
A finite element (FE) method based on the generalized backward differentiation θ formula (generalized BDF2-θ) was presented to solve nonlinear distributed-order time-fractional hyperbolic wave equations. The temporal direction was approximated with the generalized BDF2-θ to get the FE fully discrete scheme. The proposed model with high-order temporal derivatives was transformed into a coupled system including 2 lower-order equations. The stability of the proposed FE scheme and the optimal error estimates for 2 functions u and p were discussed. Several numerical examples indicate the feasibility and efficiency of the schemes.
- nonlinear distributed-order time-fractional hyperbolic wave equation /
- FE method /
- generalized BDF2-θ /
- stability /
- error estimate /
- numerical simulation

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参考文献(45)

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非线性时间分布阶双曲波动方程的广义BDF2-θ有限元方法

doi: 10.21656/1000-0887.450013

作者简介:
侯雅馨(1991—)，女，讲师，博士(E-mail: houyaxin@imut.edu.cn)；刘洋(1980—)，男，教授，博士，博士生导师(通讯作者. E-mail: mathliuyang@imu.edu.cn)；李宏(1973—)，女，教授，博士，博士生导师(E-mail: smslh@imu.edu.cn).

通讯作者:
刘洋(1980—)，男，教授，博士，博士生导师(通讯作者. E-mail: mathliuyang@imu.edu.cn).

计量

A Generalized BDF2-θ Finite Element Method for Nonlinear Distributed-Order Time-Fractional Hyperbolic Wave Equations

计量

目录

留言板

非线性时间分布阶双曲波动方程的广义BDF2-θ有限元方法

doi: 10.21656/1000-0887.450013

作者简介: 侯雅馨(1991—)，女，讲师，博士(E-mail: houyaxin@imut.edu.cn)；刘洋(1980—)，男，教授，博士，博士生导师(通讯作者. E-mail: mathliuyang@imu.edu.cn)；李宏(1973—)，女，教授，博士，博士生导师(E-mail: smslh@imu.edu.cn).

通讯作者: 刘洋(1980—)，男，教授，博士，博士生导师(通讯作者. E-mail: mathliuyang@imu.edu.cn).

计量

出版历程

A Generalized BDF2-θ Finite Element Method for Nonlinear Distributed-Order Time-Fractional Hyperbolic Wave Equations

计量

出版历程

目录

作者简介:
侯雅馨(1991—)，女，讲师，博士(E-mail: houyaxin@imut.edu.cn)；刘洋(1980—)，男，教授，博士，博士生导师(通讯作者. E-mail: mathliuyang@imu.edu.cn)；李宏(1973—)，女，教授，博士，博士生导师(E-mail: smslh@imu.edu.cn).

通讯作者:
刘洋(1980—)，男，教授，博士，博士生导师(通讯作者. E-mail: mathliuyang@imu.edu.cn).