基于RBFNN和PSO求解第二类Volterra积分方程的混合方法

J4 ›› 2010, Vol. 07 ›› Issue (4): 658-661.

基于RBFNN和PSO求解第二类Volterra积分方程的混合方法

郭新辰¹, |吴希¹, 陈书坤¹, 吴春国²

1. 东北电力大学理学院, 吉林吉林 132012； 2. 吉林大学计算机科学与技术学院, 符号计算与知识工程教育部重点实验室, 长春 130012

收稿日期:2009-11-12 出版日期:2010-07-26 发布日期:2011-06-14
通讯作者: 郭新辰 E-mail:neduer@163.com

Hybird Method Based on RBFNN and PSO for Solving LinearVolterra Integral Equations of the Second Kind

GUO Xinchen¹, WU Xi¹, CHEN Shukun¹, WU Chunguo²

1. College of Science, Northeast Dianli University, Jilin 132012, Jilin Province, China;2. College of Computer Science and Technology, Key Laboratory of Symbolic Computation and KnowledgeEngineering of Ministry of Education, Jilin University, Changchun 130012, China

Received:2009-11-12 Online:2010-07-26 Published:2011-06-14
Contact: GUO Xinchen E-mail:neduer@163.com

摘要/Abstract

摘要：

提出一种基于RBFNNs和PSO求解第二类Volterra积分方程的混合方法. 先将积分区间离散化为点集, 并代入积分方程得到方程组, 再利用RBF神经网络逼近积分方程中的未知函数, 将所求解问题转化为残差平方和的极小化问题. 利用PSO算法求解残差平方和的极小化优化问题, 得到RBF神经网络的参数, 即得问题的逼近解. 数值实验表明, 该方法可行有效.

关键词: 径向基神经网络；粒子群优化；积分方程

Abstract:

This paper presents a hybrid method based on radial basis function neural networks (RBFNN) and particle swarm optimization (PSO) algori
thm for solving the linear integral equations of the second kind of Volterra. Firstly, the integral interval is discretized into a point set. And the discretized points in the set are substituted into the equation to obtain equations. RBFNN is applied to approximating the unknown function of equations, and the solved problem can be turned into optimum problem which is solved by PSO algorithm for the advantage of PSO. Therefore, the parameters of neural networks, namely, the approximate solution, are found. Finally, numerical experiments are performed and the results show that our method is feasible.

Key words: radial based function netural networks(RBFNN), particle swarm optimization(PSO), integral equation

中图分类号:

TP303

郭新辰, 吴希, 陈书坤, 吴春国. 基于RBFNN和PSO求解第二类Volterra积分方程的混合方法[J]. J4, 2010, 07(4): 658-661.

GUO Xin-Chen, Tun-Xi, CHEN Shu-Kun, TUN Chun-Guo. Hybird Method Based on RBFNN and PSO for Solving LinearVolterra Integral Equations of the Second Kind[J]. J4, 2010, 07(4): 658-661.