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Neural Processing Letters
Erschienen in: Neural Processing Letters 3/2020

29.03.2020

Legendre Neural Network Method for Several Classes of Singularly Perturbed Differential Equations Based on Mapping and Piecewise Optimization Technology

verfasst von: Hongliang Liu, Baixue Xing, Zhen Wang, Lijuan Li

Erschienen in: Neural Processing Letters | Ausgabe 3/2020

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Abstract

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.
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Metadaten
Titel
Legendre Neural Network Method for Several Classes of Singularly Perturbed Differential Equations Based on Mapping and Piecewise Optimization Technology
verfasst von
Hongliang Liu
Baixue Xing
Zhen Wang
Lijuan Li
Publikationsdatum
29.03.2020
Verlag
Springer US
Erschienen in
Neural Processing Letters / Ausgabe 3/2020
Print ISSN: 1370-4621
Elektronische ISSN: 1573-773X
DOI
https://doi.org/10.1007/s11063-020-10232-9

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