Theoretical scheme on numerical conformal mapping of unbounded multiply connected domain by fundamental solutions method (Q1585724)

The authors describe the `fundamental solutions method' for the approximate solution of a Dirichlet or conformal mapping problem, for a bounded or unbounded domain \(D\) which is bounded by Jordan curves \(\gamma_j\). In the Dirichlet case, one approximates by \(H_n(z)= \alpha_0+ \sum^n_{k=1} \alpha_k \log |1-{z_{n,k}\over z}|\) if \(D\) is unbounded and the \(\alpha_k\) are the unknown charges at \(z_{n,k}\) which are points away from \(\cup\gamma_j\). A linear system for the \(\alpha_k\) has to be solved. Similarly in the bounded case and in the conformal map from \(D\) onto a radial or circular slit domain. Numerical experiments are announced. The authors also give a short introduction to weighted polynomials, weighted capacity etc. although this is not used in the paper.