A multi-domain pseudospectral collocation scheme for the approximation of linear fourth-order differential equations in one and two dimensions is presented. A complete analysis of the scheme is provided and error estimates are proved for the one-dimensional problem. An efficient preconditioner based on a low-order finite-difference approximation to the same differential operator is proposed. The extension of the method to the biharmonic equation in two dimensions is discussed and results are presented for a problem defined in a non-rectangular domain.
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