Some comments on the ill-conditioning of the method of fundamental solutions

In this paper, we consider the accuracy and stability of implementing the method of fundamental solutions. In contrast to the results shown in [5], we find that Gaussian elimination can be used reliably to solve the MFS equations and the use of the singular value decomposition shows no improvement over Gaussian elimination provided that the boundary condition is non-noisy. However, for noisy boundary conditions, there is evidence that the singular value decomposition with truncation is more accurate than Gaussian elimination.