Asymptotic stability of the fundamental solution method (Q1184127)

The Dirichlet problem for the Laplace equation is considered in the circle \(| x|<\rho\). The solution is approximated by a sum \(c_ 1G(x,y_ 1)+\dots+c_ nG(x,y_ n)\) with \(G(x,y)\) being the Green function and the points \(y_ 1,\dots,y_ n\) are such that \(| y_ k|=R >\rho\). The coefficients \(c_ k\) are found from the collocation system \(Ac=g\). An asymptotic estimate for the vector \(u=\Lambda c\) of the type \(\| u\| \leq Kn\| g\|\) is proved with norms related to the space \(R^ n\).