Fourth-order Compact Iterative Scheme for the Two-dimensional Time Fractional Sub-diffusion Equations

The fractional diffusion equation is an important mathematical model for describing phenomena of anomalous diffusion in transport processes. A high-order compact iterative scheme is formulated in solving the two-dimensional time fractional sub-diffusion equation. The spatial derivative is evaluated using Crank-Nicolson scheme with a fourth-order compact approximation and the Caputo derivative is used for the time fractional derivative to obtain a discrete implicit scheme. The order of convergence for the proposed method will be shown to be of . Numerical examples are provided to verify the high-order accuracy solutions of the proposed scheme.