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Legendre Neural Network for Solving Linear Variable Coefficients Delay Differential-Algebraic Equations with Weak Discontinuities

Legendre Neural Network for Solving Linear Variable Coefficients Delay Differential-Algebraic Equations with Weak Discontinuities
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Year:    2021

Author:    Hongliang Liu, Jingwen Song, Huini Liu, Jie Xu, Lijuan Li

Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 1 : pp. 101–118

Abstract

In this paper, we propose a novel Legendre neural network combined with the extreme learning machine algorithm to solve variable coefficients linear delay differential-algebraic equations with weak discontinuities. First, the solution interval is divided into multiple subintervals by weak discontinuity points. Then, Legendre neural network is used to eliminate the  hidden layer by expanding the input pattern using Legendre polynomials on each subinterval. Finally, the parameters of the neural network are obtained by training with the extreme learning machine. The numerical examples show that the proposed method can effectively deal with the difficulty of numerical simulation caused by the discontinuities.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2019-0281

Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 1 : pp. 101–118

Published online:    2021-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Convergence delay differential-algebraic equations Legendre activation function neural network.

Author Details

Hongliang Liu

Jingwen Song

Huini Liu

Jie Xu

Lijuan Li

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