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Solving high‐order partial differential equations with indirect radial basis function networks
Author(s) -
MaiDuy N.,
Tanner R. I.
Publication year - 2005
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1332
Subject(s) - biharmonic equation , radial basis function , partial differential equation , mathematics , boundary value problem , function (biology) , partial derivative , artificial neural network , mathematical analysis , computer science , artificial intelligence , evolutionary biology , biology
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 of 10 7 . Copyright © 2005 John Wiley & Sons, Ltd.