TY - JOUR
TI - Implicit local radial basis function method for solving two-dimensional time fractional diffusion equations
AU - Wei Song
AU - Chen Wen
AU - Hon Yiu-Chung
JN - Thermal Science
PY - 2015
VL - 19
IS - 11
SP - 59
EP - 67
PT - Article
AB - 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.