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A spectral collocation technique based on integrated Chebyshev polynomials for biharmonic problems in irregular domains. (English) Zbl 1167.65454
Summary: An integral collocation approach based on Chebyshev polynomials for numerically solving biharmonic equations [N. Mai-Duy, R.I. Tanner, J. Comput. Appl. Math. 201, No. 1, 30–47 (2007; Zbl 1110.65112)] is further developed for the case of irregularly shaped domains. The problem domain is embedded in a domain of regular shape, which facilitates the use of tensor product grids. Two relevant important issues, namely the description of the boundary of the domain on a tensor product grid and the imposition of double boundary conditions, are handled effectively by means of integration constants. Several schemes of the integral collocation formulation are proposed, and their performances are numerically investigated through the interpolation of a function and the solution of 1D and 2D biharmonic problems. Results obtained show that they yield spectral accuracy.
65N35Spectral, collocation and related methods (BVP of PDE)
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