Boundary solution of Poisson's equation using radial basis function collocated on Gaussian quadrature nodes

In the solution of Poisson's equation using either the dual reciprocity bou ndary element method or the method of fundamental solution, radial basis fu nctions (RBFs) are used to approximate the right-hand side of the governing partial differential equation to eliminate the domain integration. This pa per shows that if the RBF interpolation is collocated on the Gaussian quadr ature nodes, we seem to observe superconvergence behaviour. This behaviour is demonstrated using a series of numerical examples. Copyright (C) 2001 Jo hn Wiley & Sons, Ltd.