East Asian J. Appl. Math., 13 (2023), pp. 230-245.
Published online: 2023-04
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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.
}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.2022-064.210722 }, url = {http://global-sci.org/intro/article_detail/eajam/21646.html} }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.