An extension of the singular boundary method for solving two dimensional time fractional diffusion equations

In this paper, singular boundary method (SBM) in conjunction with the dual reciprocity method (DRM) is extended to the solution of constant and variable order time fractional diffusion equations (TFDEs). In this procedure, finite difference method breaks down the time domain and reduces the time fractional diffusion equation into a sequence of boundary value problems in inhomogeneous Helmholtz-type equations. Then SBM-DRM is applied to space semi-discretization of these types of equations, in a two step process. First, DRM, which is a popular meshless method based on radial basis functions (RBFs), is applied to obtain the particular solution. After evaluating the particular solution, singular boundary method can be employed to evaluate the homogeneous solution. To consider the accuracy and efficiency of the presented method, some benchmark problems subjected to the Dirichlet and Neumann boundaries are examined on regular and irregular geometries.