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

Author

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  • Ji, Cui-cui
  • Sun, Zhi-zhong

Abstract

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).

Suggested Citation

  • Ji, Cui-cui & Sun, Zhi-zhong, 2015. "The high-order compact numerical algorithms for the two-dimensional fractional sub-diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 775-791.
    • Handle: RePEc:eee:apmaco:v:269:y:2015:i:c:p:775-791
    DOI: 10.1016/j.amc.2015.07.088
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    Cited by:

    1. Ren, Lei & Wang, Yuan-Ming, 2017. "A fourth-order extrapolated compact difference method for time-fractional convection-reaction-diffusion equations with spatially variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 1-22.
    2. Li, Xuhao & Wong, Patricia J.Y., 2019. "Non-polynomial spline approach in two-dimensional fractional sub-diffusion problems," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 222-242.

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