A new theoretical error estimate of the method of fundamental solutions applied to reduced wave problems in the exterior region of a disk

In this paper, we present a mathematical study of the method of fundamental solutions (MFS) applied to reduced wave problems with Dirichlet boundary conditions in the exterior domain of a disk. A theorem in this paper shows that the MFS with N source points in equi-distantly equally phased arrangement with assignment parameter q ( 0 < q < 1 ) , which characterizes the position of the source points and the collocation points, gives an approximate solution with error of O ( q N ) if the Fourier coefficients of the boundary data decay exponentially. This error estimate is an extension of the results of the previous studies. Numerical examples make good agreements with the results of the theoretical study.