Zeitschrift für Analysis und ihre Anwendungen
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Published online: 1987-02-28
A New Computer-Assisted Analytic Method for the Dirichlet and Neumann ProblemsHerbert H. Snyder and Ralph W. Wilkerson
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 Zaremba and 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.
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Snyder Herbert, Wilkerson Ralph: A New Computer-Assisted Analytic Method for the Dirichlet and Neumann Problems. Z. Anal. Anwend. 6 (1987), 93-96. doi: 10.4171/ZAA/232