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A spectral collocation method based on integrated Chebyshev polynomials for two-dimensional biharmonic boundary-value problems. (English) Zbl 1110.65112
Summary: 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.

65N35Spectral, collocation and related methods (BVP of PDE)
35J40Higher order elliptic equations, boundary value problems
65N12Stability and convergence of numerical methods (BVP of PDE)
Full Text: DOI
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