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

  • Rui Du (a1), Zhao-peng Hao (a1) and Zhi-zhong Sun (a1)

Abstract

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.

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Corresponding author

*Corresponding author. Email addresses:rdu@seu.edu.cn (R. Du), haochpeng@126.com (Z. Hao), zzsun@seu.edu.cn (Z. Sun)

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

  • Rui Du (a1), Zhao-peng Hao (a1) and Zhi-zhong Sun (a1)

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