Numerical comparisons of two meshless methods using radial basis functions

The recent advance in the development of various kinds of meshless methods for solving partial differential equations has drawn attention of many researchers in science and engineering. One of the domain-type meshless methods is obtained by simply applying the radial basis functions (RBFs) as a direct collocation, which has shown to be effective in solving complicated physical problems with irregular domains. More recently, a boundary-type meshless method that combines the method of fundamental solutions and the dual reciprocity method with the RBFs has been developed. In this paper, the performances of these two meshless methods are compared and evaluated. Numerical results indicate that these two methods provide a similar optimal accuracy in solving both 2D Poisson's and parabolic equations. (C) 2002 Published by Elsevier Science Ltd.