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The satisfactory location for the sources outside the closure of the domain of the problem under consideration remains one of the major issues in the application of the method of fundamental solutions(MFS).In this presentation we investigate this issue by means of two algorithms,one based on the satisfaction of the boundary conditions and one based on the leave-one-out cross validation algorithm.By applying these algorithms to several numerical examples for the Laplace and biharmonic equations in a variety of geometries in two and three dimensions,we obtain locations of the sources which lead to highly accurate results,at a relatively low cost.