Fractional diffusion equations by the Kansa method

This study makes the first attempt to apply the Kansa method in the solution of the time fractional diffusion equations, in which the MultiQuadrics and thin plate spline serve as the radial basis function. In the discretization formulation, the finite difference scheme and the Kansa method are respectively used to discretize time fractional derivative and spatial derivative terms. The numerical solutions of one- and two-dimensional cases are presented and discussed, which agree well with the corresponding analytical solution. (C) 2009 Elsevier Ltd. All rights reserved.