HIGH-ORDER NUMERICAL METHOD FOR SOLVING A SPACE DISTRIBUTED-ORDER TIME-FRACTIONAL DIFFUSION EQUATION

doi:10.1007/s10473-021-0311-1

Abstract

Abstract: This article proposes a high-order numerical method for a space distributed-order time-fractional diffusion equation. First, we use the mid-point quadrature rule to transform the space distributed-order term into multi-term fractional derivatives. Second, based on the piecewise-quadratic polynomials, we construct the nodal basis functions, and then discretize the multi-term fractional equation by the finite volume method. For the time-fractional derivative, the finite difference method is used. Finally, the iterative scheme is proved to be unconditionally stable and convergent with the accuracy $O(\sigma^2+\tau^{2-\beta}+h^3)$, where $\tau$ and $h$ are the time step size and the space step size, respectively. A numerical example is presented to verify the effectiveness of the proposed method.

Key words: Space distributed-order equation, time-fractional diffusion equation, piecewise-quadratic polynomials, finite volume method, stability and convergence

CLC Number:

35R11

Jing LI, Yingying YANG, Yingjun JIANG, Libo FENG, Boling GUO. HIGH-ORDER NUMERICAL METHOD FOR SOLVING A SPACE DISTRIBUTED-ORDER TIME-FRACTIONAL DIFFUSION EQUATION[J].Acta mathematica scientia,Series B, 2021, 41(3): 801-826.

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