A new computer-assisted analytic method for the Dirichlet and Neumann problems
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.
scientific article; zbMATH DE number 4024712