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Solving high order ordinary differential equations with radial basis function networks
Author(s) -
MaiDuy N.
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.1220
Subject(s) - ordinary differential equation , radial basis function , ode , collocation (remote sensing) , collocation method , convergence (economics) , mathematics , function (biology) , basis (linear algebra) , process (computing) , orthogonal collocation , differential equation , basis function , rate of convergence , computer science , mathematical analysis , artificial neural network , geometry , artificial intelligence , key (lock) , computer security , evolutionary biology , economic growth , economics , biology , operating system , machine learning
Abstract This paper is concerned with the application of radial basis function networks (RBFNs) for numerical solution of high order ordinary differential equations (ODEs). Two unsymmetric RBF collocation schemes, namely the usual direct approach based on a differentiation process and the proposed indirect approach based on an integration process, are developed to solve high order ODEs directly and the latter is found to be considerably superior to the former. Good accuracy and high rate of convergence are obtained with the proposed indirect method. Copyright © 2004 John Wiley & Sons, Ltd.