Year: 2023
Author: Liujun Meng, Xuelin Zhang, Hanquan Wang
East Asian Journal on Applied Mathematics, Vol. 13 (2023), Iss. 2 : pp. 230–245
Abstract
A Chebyshev polynomial neural network for solving boundary value problems for one- and two-dimensional partial differential equations is constructed. In particular, the input parameters are expanded by Chebyshev polynomials and fed into the network. A loss function is constructed, and approximate solutions are determined by minimizing the loss function. Elliptic equations are used to test a Chebyshev polynomial neural network solver. The numerical examples illustrate the high accuracy of the method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.2022-064.210722
East Asian Journal on Applied Mathematics, Vol. 13 (2023), Iss. 2 : pp. 230–245
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Chebyshev polynomial neural network elliptic equation deep learning.