A spectral collocation method based on integrated Chebyshev polynomials for two-dimensional biharmonic boundary-value problems |
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Authors: | N Mai-Duy RI Tanner |
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Institution: | School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006, Australia |
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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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Keywords: | Spectral collocation methods Biharmonic problems Multiple boundary conditions Integrated Chebyshev polynomials |
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