Abstract
Using the coupled approach, we formulate a fourth order finite difference scheme for the solution of the Dirichlet biharmonic problem on the unit square. On an N × N uniform partition of the square the scheme is solved at a cost O(N 2 log2 N)+m8N 2 using fast Fourier transforms and m iterations of the preconditioned conjugate gradient method. Numerical tests confirm the fourth order accuracy of the scheme at the partition nodes with m proportional to log2 N.
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