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