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1 results

  • Lubich Second-Order Methods for Distributed-Order Time-Fractional Differential Equations with Smooth Solutions

  • Rui Du, Zhao-peng Hao, Zhi-zhong Sun
  • Journal:
    East Asian Journal on Applied Mathematics / Volume 6 / Issue 2 / May 2016
    Published online by Cambridge University Press:
    12 May 2016, pp. 131-151
    Print publication:
    May 2016

  • This article is devoted to the study of some high-order difference schemes for the distributed-order time-fractional equations in both one and two space dimensions. Based on the composite Simpson formula and Lubich second-order operator, a difference scheme is constructed with convergence in the L1(L∞)-norm for the one-dimensional case, where τ,h and σ are the respective step sizes in time, space and distributed-order. Unconditional stability and convergence are proven. An ADI difference scheme is also derived for the two-dimensional case, and proven to be unconditionally stable and convergent in the L1(L∞)-norm, where h1 and h2 are the spatial step sizes. Some numerical examples are also given to demonstrate our theoretical results.