摘要
为提高偏微分方程的计算求解精度,设计了以多元二次径向基神经网络为求解单元的偏微分计算方法,给出了多元二次径向基神经网络的具体求解结构,并以此神经网络为求解基础,给出了具体的偏微分计算步骤.通过具体的偏微分求解实例验证方法的有效性,并以3种不同设计样本数构建的多元二次径向基神经网络为计算单元,从实例求解所需的计算时间以及解的精度作对比,结果表明,采用基于多元二次径向基神经网络的偏微分方程求解方法具有求解精度高以及计算效率低等特点.
In order to improve the solving precision of partial differential equations, this paper designs a solving method of partial differential equations which regards multiquadratic radial basis neural network as solving unit, and gives the concrete structure of multiquadratic radial basis neural network. At the same time, a specific solving step of partial differential equations calculation on the basis of the neural network structure is given. Using an example of partial differential equation to verify the validity of this method and comparing the tested results with the solving time and the solution precision in three different design sample size of constructing multiple quadratic radial basis neural network, comparison results indicate that the solving method of partial differential equations based on multiquadratic radial basis neural network has many characteristics such as higher solution accuracy, lower computational efficiency and so on.
出处
《数学的实践与认识》
CSCD
北大核心
2014年第7期260-265,共6页
Mathematics in Practice and Theory
基金
河南省教育厅科学技术研究重点项目(14A520001)
河南省教师教育课程改革研究重点项目(2013JSJYZD-025)
关键词
多元二次径向基函数
神经网络
偏微分方程
求解方法
multiquadric radial basis function
neural networks
partial differential equationssolving method
