Euler基神经网络求解二维分数阶积分微分方程  

Euler based neural networks for solving two-dimensional fractionalintegral-differential equations

作　　者：郭安祺 杨刘盼 邵新平 GUO Anqi;YANG Liupan;SHAO Xinping(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）》2023年第5期66-74,共9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：通过使用序列性输入结构优化输入层以及构造微分算子,提出一种基于Euler多项式的基函数神经网络求解二维分数阶Fredholm型积分-偏微分方程的方法。给出多项式序列可一致逼近二元函数的理论证明,为算法提供理论基础,最后通过数值实验的结果验证了该算法的可行性与精确性。The sequential input structure is used to optimize the input layer,and a basis function neural network based on Euler polynomials is proposed to solve two-dimensional fractional Fredholm type integral partial differential equations.It is proved that polynomial sequences can uniformly approximate binary functions,which provides a theoretical basis for the algorithm.Finally,the feasibility and accuracy of the algorithm are verified by numerical experiments.

关 键 词：神经网络 EULER多项式 函数逼近 二维Fredholm积分微分方程 分数阶导数 

分 类 号：O24[理学—计算数学]