A spectral collocation method based on integrated Chebyshev polynomials for two-dimensional biharmonic boundary-value problems

Mai-Duy, Nam and Tanner, Roger I. (2007) A spectral collocation method based on integrated Chebyshev polynomials for two-dimensional biharmonic boundary-value problems. Journal of Computational and Applied Mathematics, 201 (1). pp. 30-47. ISSN 0377-0427

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Abstract

This paper reports a new spectral collocation method for numerically solving two-dimensional biharmonic boundary-value problems. The construction of the Chebyshev approximations is based on integration rather than conventional differentiation. This use of integration allows: (i) the imposition of the governing equation at the whole set of grid points including the boundary points and (ii) the straightforward implementation of multiple boundary conditions. The performance of the proposed method is investigated by considering several biharmonic problems of first and second kinds; more accurate results and higher convergence rates are achieved than with conventional differential methods.


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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 Feb 2008 01:06
Last Modified: 02 Jul 2013 22:54
Uncontrolled Keywords: spectral collocation methods; biharmonic problems; multiple boundary conditions; integrated Chebyshev polynomials
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 > 010106 Lie Groups, Harmonic and Fourier Analysis
01 Mathematical Sciences > 0102 Applied Mathematics > 010207 Theoretical and Applied Mechanics
Socio-Economic Objective (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
Identification Number or DOI: doi: 10.1016/j.cam.2006.01.030
URI: http://eprints.usq.edu.au/id/eprint/3567

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