A high-order exponential ADI scheme for two dimensional time fractional convection–diffusion equations

In this paper, a high order compact exponential alternating direction implicit (ADI) scheme for two dimensional fractional convection–diffusion equations is proposed with O(τ3−γ+h14+h24) accuracy, where τ,h1,h2 are the temporal and spatial step sizes respectively. The convergence of the finite difference scheme is studied using its matrix form by the energy method. Difficulty arising from the convection term is overcome by an analysis based on the eigenvalue decomposition of nonsymmetric tridiagonal matrices.