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Numerical Algorithms

, Volume 74, Issue 3, pp 675–697 | Cite as

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

  • Guang-hua Gao
  • Zhi-zhong Sun
Original Paper

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 2γ 2) and O(τ 2 + h 4γ 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.

Keywords

Distributed order Fractional derivative Difference scheme Stability Convergence 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.College of ScienceNanjing University of Posts and TelecommunicationsNanjingPeople’s Republic of China
  2. 2.Department of MathematicsSoutheast UniversityNanjingPeople’s Republic of China

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