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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 γ lies in the interval γ(0,1 2). A correction term is added to maintain high accuracy when [1 2,1). Numerical results are provided to verify the accuracy and efficiency of the proposed algorithm.
MSC:
65M06Finite difference methods (IVP of PDE)
35K05Heat equation
35R11Fractional partial differential equations
65M12Stability and convergence of numerical methods (IVP of PDE)
65M15Error bounds (IVP of PDE)
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