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.
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 newway of solving the strongly nonlinear Bratu-type equations.
出处
《应用数学和力学》
CSCD
北大核心
2016年第6期617-625,共9页
Applied Mathematics and Mechanics
基金
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)
关键词
径向基函数
Bratu型方程
强非线性
数值解
radial basis function
Bratu-type equation
strong nonlinearity
numerical solution
