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 L 2 norm convergence of the ADI scheme are proved rigorously. Numerical results are presented to support our theoretical analysis.