分数阶Fornberg-Whitham方程及其改进方程的变分迭代解

鲍四元; 邓子辰

doi:10.3879/j.issn.1000-0887.2013.12.002

分数阶Fornberg-Whitham方程及其改进方程的变分迭代解

doi: 10.3879/j.issn.1000-0887.2013.12.002

鲍四元¹,
邓子辰^2,3

¹苏州科技学院土木工程学院工程力学系, 江苏苏州 215011;²西北工业大学工程力学系,西安 710072;³大连理工大学工业装备结构分析国家重点实验室, 辽宁大连 116023

基金项目: 国家自然科学基金资助项目(11202146)

详细信息

作者简介:
鲍四元（1980—），男，安徽人，副教授，博士(通讯作者. E-mail: bsiyuan@126.com)；邓子辰(1964—),男,西安人，教授,博士生导师(E-mail: dweifan@nwpu.edu.cn).

中图分类号: O175.29
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出版历程
- 收稿日期: 2013-08-27
- 修回日期: 2013-10-30
- 刊出日期: 2013-12-16

Variational Iteration Solutions for Fractional FornbergWhitham Equation and Its Modified Equation

BAO Si-yuan¹,
DENG Zi-chen^2,3

¹Department of Engineering Mechanics, School of Civil Engineering,Suzhou University of Science and Technology, Suzhou, Jiangsu 215011, P.R.China;²Department of Engineering Mechanics, Northwestern Polytechnical University, Xi’an 710072, P.R.China;³State Key Laboratory of Structural Analysis of Industrial Equipment,Dalian University of Technology, Dalian, Liaoning 116023, P.R.China

Funds: The National Natural Science Foundation of China(11202146)

摘要

摘要: 给出分数阶FornbergWhitham方程(FFW)并把其中非线性项uu_x换为u²u_x后所得的改进Fornberg-Whitham方程的解．使用了分数阶变分迭代法(fractional variational iteration method，FVIM)，其中Lagrange乘子由泛函和Laplace变换确定．讨论了分数阶次的数值在两种情况下FFW方程的解，因为确定FFW方程中时间微分的阶次需要比较原方程中含时间的两个微分的阶次．最后，给出两个使用分数阶变分迭代法的算例．算例结果证明了所提方法的有效性
- 分数阶Fornberg-Whitham方程 /
- 分数阶变分迭代法 /
- Lagrange乘子 /
- 近似解 /
- 初值问题
Abstract: The solutions to the fractional FornbergWhitham (FFW) equation and the modified FFW equation generated by change of one nonlinear term uu_x with u²u_x were presented. The fractional variational iteration method (FVIM) was used, in which the Lagrange multiplier was determined with the variational function and the Laplace transformation. Two cases were discussed respectively for the FFW equation because the order of time differentiation was determined through comparison of the two derivatives’orders in the fractional differential equation. Finally, two numerical examples of the FVIM solution were given. The computational results demonstrate the high efficiency of the presented method.
- fractional FornbergWhitham equation /
- fractional variational iteration method /
- Lagrange multiplier /
- approximate solution /
- initial value problem

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参考文献(34)

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分数阶Fornberg-Whitham方程及其改进方程的变分迭代解

doi: 10.3879/j.issn.1000-0887.2013.12.002

作者简介:
鲍四元（1980—），男，安徽人，副教授，博士(通讯作者. E-mail: bsiyuan@126.com)；邓子辰(1964—),男,西安人，教授,博士生导师(E-mail: dweifan@nwpu.edu.cn).

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Variational Iteration Solutions for Fractional FornbergWhitham Equation and Its Modified Equation

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留言板

分数阶Fornberg-Whitham方程及其改进方程的变分迭代解

doi: 10.3879/j.issn.1000-0887.2013.12.002

作者简介: 鲍四元（1980—），男，安徽人，副教授，博士(通讯作者. E-mail: bsiyuan@126.com)；邓子辰(1964—),男,西安人，教授,博士生导师(E-mail: dweifan@nwpu.edu.cn).

计量

出版历程

Variational Iteration Solutions for Fractional FornbergWhitham Equation and Its Modified Equation

计量

出版历程

目录

作者简介:
鲍四元（1980—），男，安徽人，副教授，博士(通讯作者. E-mail: bsiyuan@126.com)；邓子辰(1964—),男,西安人，教授,博士生导师(E-mail: dweifan@nwpu.edu.cn).