求解Bratu型方程的径向基函数逼近法

洪文强; 徐绩青; 许锡宾; 张春; 周世良

doi:10.3879/j.issn.1000-0887.2016.06.007

求解Bratu型方程的径向基函数逼近法

doi: 10.3879/j.issn.1000-0887.2016.06.007

洪文强¹,
徐绩青^1,2,
许锡宾^1,2,3,
张春³,
周世良^1,2

¹重庆交通大学河海学院, 重庆 400074;²重庆交通大学国家内河航道整治工程技术研究中心,水利水运工程教育部重点实验室, 重庆400074;³重庆建筑工程职业学院, 重庆 400072

基金项目: 重庆市教委科学技术研究项目（KJ100417）；交通运输部应用基础研究项目（2014329814070）

详细信息

作者简介:
洪文强（1990—），男，硕士生（E-mail: 350720030@qq.com);徐绩青（1974—），男，博士（通讯作者. E-mail: plappk@sina.com).

中图分类号: TV312
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- 被引次数: 0
出版历程
- 收稿日期: 2015-12-24
- 修回日期: 2016-02-15
- 刊出日期: 2016-06-15

The Radial Basis Function Approximation Method for Solving Bratu-Type Equations

¹School of River & Ocean Engineering, Chongqing Jiaotong University,Chongqing 400074, P.R.China;²National Engineering Research Center for Inland Waterway Regulation;Key Laboratory of Hydraulic & Waterway Engineering of the Ministry of Education, Chongqing Jiaotong University, Chongqing 400074, P.R.China;³Chongqing Jianzhu College, Chongqing 400072, P.R.China

Funds: The National Natural Science Foundation of China，The National Basic Research Program of China (973 Program)

摘要

摘要: 基于径向基函数可以逼近几乎所有函数的强大逼近功能，借鉴弹塑性静力学的处理方法,提出位移、速度、加速度联合插值的径向基函数表达式，结合MATLAB数值软件进行计算机编程，成功求解了Bratu型强非线性方程，并给出相应的相对误差.通过分析几种典型的算例，并将计算结果与一些现有的数值分析法得到的数值解进行对比，表明了该方法的可行性和精确性，为求解强非线性Bratu型方程提供了一种新思路.
- 径向基函数 /
- Bratu型方程 /
- 强非线性 /
- 数值解
Abstract: Based on the powerful approximation capability of the radial basis function for almost all kinds of functions, and with reference to the interpolation method for elasto-plastic mechanics, the radial basis function expression of the interpolation combining displacement, velocity and acceleration was put forward. Then the MATLAB software was used for computer programming to successfully solve the strongly nonlinear Bratu-type equation, with the corresponding relative errors given and discussed. The analysis of several typical examples was conducted, where the present calculated results were compared with some of the existing numerical results as well as the exact solutions. The comparison shows the feasibility and high accuracy of the present method, which makes a new way of solving the strongly nonlinear Bratu-type equations.
- radial basis function /
- Bratu-type equation /
- strong nonlinearity /
- numerical solution

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参考文献(24)

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