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Analysis of a new finite difference/local discontinuous Galerkin method for the fractional diffusion-wave equation

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  • Wei, Leilei

Abstract

In this paper a finite difference/local discontinuous Galerkin method for the fractional diffusion-wave equation is presented and analyzed. We first propose a new finite difference method to approximate the time fractional derivatives, and give a semidiscrete scheme in time. Further we develop a fully discrete scheme for the fractional diffusion-wave equation, and prove that the method is unconditionally stable and convergent with order O(hk+1+(Δt)3−α), where k is the degree of piecewise polynomial. Extensive numerical examples are carried out to confirm the theoretical convergence rates.

Suggested Citation

  • Wei, Leilei, 2017. "Analysis of a new finite difference/local discontinuous Galerkin method for the fractional diffusion-wave equation," Applied Mathematics and Computation, Elsevier, vol. 304(C), pages 180-189.
    • Handle: RePEc:eee:apmaco:v:304:y:2017:i:c:p:180-189
    DOI: 10.1016/j.amc.2017.01.054
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    Cited by:

    1. An, Na & Huang, Chaobao & Yu, Xijun, 2019. "Error analysis of direct discontinuous Galerkin method for two-dimensional fractional diffusion-wave equation," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 148-157.
    2. Yu, Hao & Wu, Boying & Zhang, Dazhi, 2018. "A generalized Laguerre spectral Petrov–Galerkin method for the time-fractional subdiffusion equation on the semi-infinite domain," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 96-111.

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