Solving high-order partial differential equations with indirect radial basis function networks

Mai-Duy, N. and Tanner, R. I. (2005) Solving high-order partial differential equations with indirect radial basis function networks. International Journal for Numerical Methods in Engineering, 63 (11). pp. 1636-1654. ISSN 0029-5981

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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.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Deposited in accordance with the copyright policy of the publisher.
Depositing User: Dr Nam Mai-Duy
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 11 Oct 2007 01:14
Last Modified: 02 Jul 2013 22:46
Uncontrolled Keywords: radial basis functions; approximation; multiple boundary conditions; high order derivatives; high-order partial differential equations
Fields of Research (FOR2008): 01 Mathematical Sciences > 0101 Pure Mathematics > 010110 Partial Differential Equations
01 Mathematical Sciences > 0101 Pure Mathematics > 010106 Lie Groups, Harmonic and Fourier Analysis
01 Mathematical Sciences > 0102 Applied Mathematics > 010201 Approximation Theory and Asymptotic Methods
Socio-Economic Objective (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
Identification Number or DOI: doi: 10.1002/nme.1332
URI: http://eprints.usq.edu.au/id/eprint/2786

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