Convergence of the invariant scheme of the method of fundamental solutions for two-dimensional potential problems in a Jordan region

We examine the invariant scheme of the method of fundamental solutions for two-dimensional potential problems, that is, Dirichlet boundary value problems of the Laplace equation in a Jordan region, with the charge points and the collocation points obtained by a conformal mapping of the exterior of a disk to the exterior of the problem region. By a theoretical error analysis, we show that the approximate solution of the invariant scheme converges to the exact solution exponentially and some unnatural assumptions needed in the conventional scheme are removed in the convergence theorem of the invariant scheme.