D. Greenspan – Communications of the ACM

Research and Advances May 1 1972

Fast finite-difference solution of biharmonic problems

Setting the Reynolds number equal to zero, in a method for solving the Navier-Stokes equations numerically, results in a fast numerical method for biharmonic problems. The equation is treated as a system of two second order equations and a simple smoothing process is essential for convergence. An application is made to a crack-type problem.

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Research and Advances Sep 1 1963

On the approximate solution of Δ u=F(u)

Three-dimensional Dirichlet problems for &Dgr;u = F(u), Fu &gE; 0, are treated numerically by an exceptionally fast, exceptionally accurate numerical method. Programming details, numerous examples and mathematical theory are supplied. Extension of the method in a natural way to n-dimensional problems is indicated by means of a 4-dimensional example.

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