A Chebyshev Polynomial Neural Network Solver for Boundary Value Problems of Elliptic Equations

A Chebyshev Polynomial Neural Network Solver for Boundary Value Problems of Elliptic Equations

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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.

Author Details

Liujun Meng

Xuelin Zhang

Hanquan Wang