The BEM and DRBEM schemes for the numerical solution of the two-dimensional time-fractional diffusion-wave equations

In this paper we apply the boundary elements method (BEM) and the dual reciprocity boundary elements method (DRBEM) for the numerical solution of two-dimensional time-fractional partial differential equations (TFPDEs). The fractional derivative of problem is described in the Caputo sense. In BEM, the main equation deduces to solving the Helmholtz equation in each time step. Therefore, we should compute the domain integral in each time step. So, we presented an approach to compute the domain integral with no singularity. On the other hand the DRBEM has the flexibility of discretizing only the boundary of the computational domain and evaluates the solution at any required interior point. We employ the radial basis functions (RBFs) for interpolation of the inhomogeneous and time derivative terms. The proposed method is employed for solving some problems in two--dimensions on unit square and some other complex regions to demonstrate the efficiency of the proposed method.