The high-order compact numerical algorithms for the two-dimensional fractional sub-diffusion equation

In this paper, performing the average operators on the space variables, a numerical scheme with third-order temporal convergence for the two-dimensional fractional sub-diffusion equation is considered, for which the unconditional stability and convergence in L1(L∞)-norm are strictly analyzed for α ∈ (0, 0.9569347] by using the discrete energy method. Therewith, adding small perturbation terms, we construct a compact alternating direction implicit difference scheme for the two-dimensional case. Finally, some numerical results have been given to show the computational efficiency and numerical accuracy of both schemes for all α ∈ (0, 1).