Implicit local radial basis function method for solving two-dimensional time fractional diffusion equations

Based on the recently developed local radial basis function method, we devise an implicit local radial basis function scheme, which is intrinsic mesh-free, for solving time fractional diffusion equations. In this paper the L1 scheme and the local radial basis function method are applied for temporal and spatial discretization, respectively, in which the time-marching iteration is performed implicitly. The robustness and accuracy of this proposed implicit local radial basis function method are demonstrated by the numerical example. Furthermore, the sensitivities of the shape parameter c and the number of nodes in the local sub-domain to the accuracy of numerical solutions are also investigated