Solving high-order partial differential equations with indirect radial basis function networks
Article
Article Title | Solving high-order partial differential equations with indirect radial basis function networks |
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ERA Journal ID | 187 |
Article Category | Article |
Authors | Mai-Duy, N. (Author) and Tanner, R. I. (Author) |
Journal Title | International Journal for Numerical Methods in Engineering |
Journal Citation | 63 (11), pp. 1636-1654 |
Number of Pages | 38 |
Year | 2005 |
Place of Publication | Bognor Regis, West Sussex. United Kingdom |
ISSN | 0029-5981 |
1097-0207 | |
Digital Object Identifier (DOI) | https://doi.org/10.1002/nme.1332 |
Web Address (URL) | http://www3.interscience.wiley.com/cgi-bin/fulltext/110473747/PDFSTART |
Abstract | This paper reports a new numerical method based on radial basis function networks (RBFNs) for solving high-order partial differential equations (PDEs). The variables and their derivatives in the governing equations are represented by integrated RBFNs. The use of integration in constructing neural networks allows the straightforward implementation of multiple boundary conditions and the accurate approximation of high-order derivatives. The proposed RBFN method is verified successfully through the solution of thin-plate bending and viscous flow problems which are governed by biharmonic equations. For thermally driven cavity flows, the solutions are obtained up to a high Rayleigh number. |
Keywords | radial basis functions; approximation; multiple boundary conditions; high order derivatives;high-order partial differential equations |
ANZSRC Field of Research 2020 | 490410. Partial differential equations |
490406. Lie groups, harmonic and Fourier analysis | |
490101. Approximation theory and asymptotic methods | |
Public Notes | File reproduced in accordance with the copyright policy of the publisher/author. |
Byline Affiliations | University of Sydney |
https://research.usq.edu.au/item/9y421/solving-high-order-partial-differential-equations-with-indirect-radial-basis-function-networks
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