Legendre Neural Network Method for Several Classes of Singularly Perturbed Differential Equations Based on Mapping and Piecewise Optimization Technology
Legendre Neural Network Method for Several Classes of Singularly Perturbed Differential Equations Based on Mapping and Piecewise Optimization Technology
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DOI：
10.1007/s11063-020-10232-9
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发表时间：
2020-03
影响因子：
3.1
通讯作者：
Hongliang Liu;Baixue Xing;Zhen Wang;Lijuan Li
中科院分区：
文献类型：
--
作者：
Hongliang Liu;Baixue Xing;Zhen Wang;Lijuan Li
本文针对几类变系数线性奇摄动初值和边值微分方程，利用映射和分段优化技术建立了一种新的神经网络模型。首先，选取勒让德多项式作为人工神经网络的激活函数，利用映射技术对原始均匀划分点进行变换，并采用分段优化技术提高计算精度。然后，利用极限学习机优化算法求解线性奇摄动微分方程。最后，数值实验表明，该方法能有效地提高计算精度。
In this paper, we develop a novel neural network model with mapping and piecewise optimization technology for several classes of the linear singularly perturbed initial value and boundary value differential equations with variable coefficients. First, the Legendre polynomials are selected as the activation function of the artificial neural network, the mapping technology is employed to transform the original uniform partition points and the piecewise optimization technology is used to improve the calculation accuracy. Then, the solution of the linear singularly perturbed differential equations is solved by using the extreme learning machine optimization algorithm. Finally, the numerical experiments show that the developed method can effectively improve the accuracy of the calculation.