基于前馈型神经网络解线性Fredholm积分-微分方程  

Solving linear fredholm integro-differential equations based on feedforward neural network

作　　者：许彩虹 邵新平 张林[1] XU Caihong;SHAO Xinping;ZHANG Lin(School of Sciences,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学理学院,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2022年第2期96-102,共7页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：国家自然科学基金资助项目(11701133)。

摘　　要：为了研究积分微分方程的数值解,构造了一种前馈型神经网络用于求解Fredholm积分微分方程近似解。首先,运用Taylor展开式近似代替未知函数,神经网络的误差由内部误差和边界误差组成。其次,应用神经网络对Taylor展开式的系数进行学习从而得到近似解。最后,与梯形求积规则(Trapezoidal Quadrature Rule,TQR)数值方法进行比较,验证了提出方法的可行性与有效性。In order to study the numerical solutions of integro-differential equations,a feedforward neural network is constructed to solve the approximate solutions of Fredholm integro-differential equations.Firstly,the Taylor expansions are used to approximately replace the unknown solution,and the errors of neural network are composed of internal error and boundary error.Secondly,the coefficients of the Taylor expansion are adjusted by the proposed neural network.Finally,by comparing with the numerical method of Trapezoidal Quadrature Rule(TQR),the feasibility and effectiveness of the method are verified.

关 键 词：Fredholm积分微分方程 前馈型神经网络 近似解 学习算法 

分 类 号：O242.2[理学—计算数学]