Alternating direction implicit Galerkin finite element method for the two-dimensional fractional diffusion-wave equation

New numerical techniques are presented for the solution of the two-dimensional fractional diffusion-wave equation with a time fractional derivative of order α(1<α<2). In these methods, Galerkin finite element is used for the spatial discretization, and, for the time stepping, new alternating direction implicit (ADI) method based on the Crank-Nicolson method are considered. The unconditional stability and L2 norm convergence of the ADI scheme are proved rigorously. Numerical results are presented to support our theoretical analysis.