Solving high order ordinary differential equations with radial basis function networks

Mai-Duy, Nam (2005) Solving high order ordinary differential equations with radial basis function networks. International Journal for Numerical Methods in Engineering, 62 (6). pp. 824-852. ISSN 0029-5981

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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.


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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: approximation; high order; derivatives; ordinary differential equations
Fields of Research (FOR2008): 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
01 Mathematical Sciences > 0101 Pure Mathematics > 010109 Ordinary Differential Equations, Difference Equations and Dynamical Systems
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.1220
URI: http://eprints.usq.edu.au/id/eprint/2785

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