Author(s)

M. Zerroukat

Abstract

A simple, mesh/grid free, numerical scheme for the solution of convection- diffusion problems is developed herein. Unlike the mesh or regular grid based methods, this scheme uses well distributed quasi-random points and approximate the solution using radial basis functions. The scheme can be seen as generalised finite differences with random points instead of a regular grid system. This allow the computation of problems with complex-shaped boundaries in higher dimensions with no extra difficulty. 1 Introduction For many years, radial basis functions have been synonymous with scattered data approximation, especially in higher dimensions. How- ever, recently there has been an increased interest in their use in solving partial differential equations (PDEs). This approach, which approximates the whole solution of the'P

Keywords