In continuation of part I [cf. the author and H. Okamoto, ibid. 35, No.3, 507-518 (1988; Zbl 0662.65100)], a theorem on convergence and rate of convergence is proved for the charge simulation method for the numerical solution of the first boundary value problem for the Laplace equation in a circle. Further convergence theorems concern the replacement of the charges by dipoles (which is advantageous), and the application of the method to the Neumann problem and to annular domains.
For the original problem (Laplace equation in a circle) several (but not all) arrangements of the collocation points are shown to yield similar results. The theorems are illustrated by quite a number of interesting numerical experiments.