RADIAL BASIS FUNCTIONS- SOME RECENT DEVELOPMENTS

Abstract. Radial basis functions (RBF) is a recent methodology for scattered data interpolation, offering possibilities for meshfree numerical solution of PDEs to spectral accuracy also on irregular domains in any number of dimensions. We briefly introduce RBFs, and then focus on some recent developments, especially with regard to the Gibbs and the Runge phenomena for RBF interpolants. The latter suggests ways to further enhance the RBF methodology for solving PDEs