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Two difference schemes for solving the one-dimensional time distributed-order fractional wave equations

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Abstract

Two difference schemes are derived for numerically solving the one-dimensional time distributed-order fractional wave equations. It is proved that the schemes are unconditionally stable and convergent in the \(L^{\infty }\) norm with the convergence orders O(τ 2 + h 2+Δγ 2) and O(τ 2 + h 4+Δγ 4), respectively, where τ,h, and Δγ are the step sizes in time, space, and distributed order. A numerical example is implemented to confirm the theoretical results.

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Authors and Affiliations

  1. College of Science, Nanjing University of Posts and Telecommunications, Nanjing, 210023, People’s Republic of China

    Guang-hua Gao

  2. Department of Mathematics, Southeast University, Nanjing, 210096, People’s Republic of China

    Zhi-zhong Sun

Authors
  1. Guang-hua Gao
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  2. Zhi-zhong Sun
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Correspondence to Guang-hua Gao.

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Gao, Gh., Sun, Zz. Two difference schemes for solving the one-dimensional time distributed-order fractional wave equations. Numer Algor 74, 675–697 (2017). https://doi.org/10.1007/s11075-016-0167-y

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