The method of fundamental solutions (MFS) and the Collocation Trefftz
method have been known as two highly effective boundary-type methods for solving
homogeneous equations. Despite many attractive features of these two methods,
they also experience different aspects of difficulty. Recent advances in the selection of
source location of the MFS and the techniques in reducing the condition number of the
Trefftz method have made significant improvement in the performance of these two
methods which have been proven to be theoretically equivalent. In this paper we will
compare the numerical performance of these two methods under various smoothness
of the boundary and boundary conditions.
Trefftz method, the method of fundamental solution, LOOCV, multiple scale method, non-harmonic boundary conditions.