Numerical Comparison of the LOOCV-MFS and the MS-CTM for 2D Equations (Advances in Applied Mathematics and Mechanics, 2018)
The method of fundamental solutions (MFS) and the Collocation Trefftzmethod have been known as two highly effective boundary-type methods for solvinghomogeneous equations. Despite many attractive features of these two methods,they also experience different aspects of difficulties. Recent advances in the selection ofsource location of the MFS and the techniques in reducing the condition number of theTrefftz method have made significant improvement in the performance of these twomethods which have been proven to be theoretically equivalent. In this paper we willcompare the numerical performance of these two methods under various smoothnessof the boundary and boundary conditions.