A second order BDF alternating direction implicit difference scheme for the two-dimensional fractional evolution equation

A second order backward differentiation formula (BDF) alternating direction implicit (ADI) difference scheme is formulated and analyzed for the two-dimensional fractional evolution equation. In this method, standard central difference approximation used for the spatial discretization and the time stepping - an alternating direction implicit scheme based on second order convolution quadrature suggested by Lubich and second order BDF are considered. The stability and convergence of the second order BDF ADI difference scheme in L2 norm are derived by the energy method. Numerical experiments in total agreement with our analysis are reported.