On Multi-Quadric Based RBF–FD Method for Second-Order Diffusion Filters

Abstract

The usual three-node approximations for the first-order spatial derivatives in the radial basis functions-based finite difference (RBF-FD) scheme allows relatively smaller time step size than the standard scheme (forward difference in time and central difference in space) in obtaining stable results. In this paper, to better mimic the continuous model, we use nine nodal points in RBF–FD approximation of first-order spatial derivatives. We then employ these approximations to solve a two-dimensional nonlinear diffusion equation from image processing. The constructed numerical scheme is shown to be stable and allows up to obtain four times bigger time step size than the standard scheme.