A new computer-assisted analytic method for the Dirichlet and Neumann problems (Q1094118)

The authors introduce a new method for the Dirichlet and Neumann problems (in \({\mathbb{R}}^ 2\) and \({\mathbb{R}}^ 3)\) based on certain theorems of S. Zaremba and S. Bergmann. With the help of a symbolic computing language (FORMAC with PL/1), the authors show how it is possible to orthonormalize a complete sequence of harmonic polynomials on the domain G of the solution. The solution is then given by an expansion in these orthonormalized polynomials. Under certain conditions on the boundary values, the expansion coefficients themselves may also be automatically calculated.