An effective spectral collocation method for the direct solution of high-order ODEs

Mai-Duy, Nam (2006) An effective spectral collocation method for the direct solution of high-order ODEs. Communications in Numerical Methods in Engineering, 22 (6). pp. 627-642. ISSN 1069-8299

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Abstract

This paper reports a new Chebyshev spectral collocation method for directly solving high-order ordinary differential equations (ODEs). The construction of the Chebyshev approximations is based on integration rather than conventional differentiation. This use of integration allows the multiple boundary conditions to be incorporated more efficiently. Numerical results show that the proposed formulation significantly improves the conditioning of the system and yields more accurate results and faster convergence rates than conventional formulations.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Author's version 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: 30 Mar 2010 10:47
Last Modified: 02 Jul 2013 23:44
Uncontrolled Keywords: spectral collocation methods; high-order ordinary differential equations; multiple boundary conditions; integrated basis-functions
Fields of Research (FOR2008): 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation
01 Mathematical Sciences > 0102 Applied Mathematics > 010203 Calculus of Variations, Systems Theory and Control Theory
Socio-Economic Objective (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
Identification Number or DOI: doi: 10.1002/cnm.841
URI: http://eprints.usq.edu.au/id/eprint/7207

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