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The discontinuous Galerkin finite element approximation of the multi-order fractional initial problems

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  • Zheng, Yunying
  • Zhao, Zhengang
  • Cui, Yanfen

Abstract

In this paper, we construct a discontinuous Galerkin finite element scheme for the multi-order fractional ordinary differential equation. The analysis of the stability shows the scheme is L2 stable. The existence and uniqueness of the numerical solution are discussed in detail. The convergence study gives the approximation orders under L2 norm and L∞ norm. Numerical examples demonstrate the effectiveness of the theoretical results. The oscillation phenomena are also found during numerical tracing a non-linear multi-order fractional initial problem.

Suggested Citation

  • Zheng, Yunying & Zhao, Zhengang & Cui, Yanfen, 2019. "The discontinuous Galerkin finite element approximation of the multi-order fractional initial problems," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 257-269.
    • Handle: RePEc:eee:apmaco:v:348:y:2019:i:c:p:257-269
    DOI: 10.1016/j.amc.2018.11.057
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    References listed on IDEAS

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    1. Balescu, R., 2007. "V-Langevin equations, continuous time random walks and fractional diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 34(1), pages 62-80.
    2. Eab, C.H. & Lim, S.C., 2010. "Fractional generalized Langevin equation approach to single-file diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(13), pages 2510-2521.
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    Cited by:

    1. Can Liu & Xinming Zhang & Boying Wu, 2020. "Quasilinearized Semi-Orthogonal B-Spline Wavelet Method for Solving Multi-Term Non-Linear Fractional Order Equations," Mathematics, MDPI, vol. 8(9), pages 1-15, September.

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