Efficient solution of the biharmonic equation

A new method for the numerical solution of the first biharmonic problem in a rectangular region is outlined. The theoretical complexity of the method is $N^2$ + O(N) storage and O($N^2$) arithmetic operations. (In order to achieve a prescribed accuracy on an N by N grid.) Numerical results from a computer code that requires a$N^2$ + b$N^2$logN + O(N) operations with b >> a, are presented using both a scalar and a vector computer. Extensions and some applications of the method for solving eigenvalue problems and certain nonlinear problems are mentioned.

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