RBF Collocation Methods As PseudospectralMethods

We show how the collocation framework that is prevalent in the radial basis function literature can be modified so that the methods can be interpreted in the framework of standard pseudospectral methods. This implies that many of the standard algorithms and strategies used for solving time-dependent as well as time-independent partial differential equations with (polynomial) pseudospectral methods can be readily adapted for the use with radial basis functions. The potential advantage of radial basis functions is that they lend themselves to complex geometries and non-uniform discretizations.