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Compact alternating direction implicit method for two-dimensional time fractional diffusion equation. (English) Zbl 1242.65158
Summary: High-order compact finite difference scheme with operator splitting technique for solving two-dimensional time fractional diffusion equation is considered in this paper. A Grünwald-Letnikov approximation is used for the Riemann-Liouville time derivative, and the second order spatial derivatives are approximated by the compact finite differences to obtain a fully discrete implicit scheme. Alternating direction implicit (ADI) method is used to split the original problem into two separate one-dimensional problems. The local truncation error is analyzed and the stability is discussed by the Fourier method. The proposed scheme is suitable when the order of the time fractional derivative $$\gamma$$ lies in the interval $$\gamma \in (0,\frac 12)$$. A correction term is added to maintain high accuracy when $$[\frac 12,1)$$. Numerical results are provided to verify the accuracy and efficiency of the proposed algorithm.

##### MSC:
 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 35K05 Heat equation 35R11 Fractional partial differential equations 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
ma2dfc; PDE2D
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