基于径向基函数神经网络的微分方程数值解

Liang Jianyu, Luo Siwei, Qi Yingjian, H. Yaping
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引用次数: 16

摘要

本文提出了一种基于多重二次径向基函数网络(rbfn)的线性常微分方程求解方法。根据利用径向基函数网络逼近函数及其导数的思想,本文提出了另一种不同于径向基函数网络的求解ODE的RBFN逼近方法。该技术可以同时确定所有参数,而无需学习过程。该技术的优点是不需要足够的数据,只依赖于域和边界。我们的结果更准确。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Numerical solution of differential equations by radial basis function neural networks
In this paper we present a method for solving linear ordinary differential equations (ODE) based on multiquadric (MQ) radial basis function networks (RBFNs). According to the thought of approximation of function and/or its derivatives by using radial basis function networks, another new RBFN approximation procedures different from are developed in this paper for solving ODE. This technique can determine all the parameters at the same time without a learning process. The advantage of this technique is that it doesn't need sufficient data, just relies on the domain and the boundary. Our results are more accurate.
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