Katsurada, Masashi; Okamoto, Hisashi A mathematical study of the charge simulation method. I. (English) Zbl 0662.65100 J. Fac. Sci., Univ. Tokyo, Sect. I A 35, No. 3, 507-518 (1988). The charge simulation method is a means to solve the first boundary value problem for the Laplace equation in a two-dimensional domain. It consists in determining N charges located outside the domain by collocation at N boundary points. The authors consider a circular domain, give a condition for unique solvability and an error estimate which shows an exponential rate of convergence for analytic boundary data. They conclude with remarks on more general domains. Reviewer: G.Stoyan Cited in 2 ReviewsCited in 58 Documents MSC: 65N35 Spectral, collocation and related methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation Keywords:fundamental solution; harmonic functions; charge simulation method; Laplace equation; collocation; error estimate; exponential rate of convergence PDFBibTeX XMLCite \textit{M. Katsurada} and \textit{H. Okamoto}, J. Fac. Sci., Univ. Tokyo, Sect. I A 35, No. 3, 507--518 (1988; Zbl 0662.65100)