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Numerical Algorithms

, Volume 77, Issue 3, pp 675–690 | Cite as

Analysis of a new finite difference/local discontinuous Galerkin method for the fractional Cattaneo equation

  • Leilei Wei
Original Paper
  • 170 Downloads

Abstract

In this paper, we first present a new finite difference scheme to approximate the time fractional derivatives, which is defined in the sense of Caputo, and give a semidiscrete scheme in time with the truncation error O((Δt)3−α ), where Δt is the time step size. Then a fully discrete scheme based on the semidiscrete scheme for the fractional Cattaneo equation in which the space direction is approximated by a local discontinuous Galerkin method is presented and analyzed. We prove that the method is unconditionally stable and convergent with order O(h k+1 + (Δt)3−α ), where k is the degree of piecewise polynomial. Numerical examples are also given to confirm the theoretical analysis.

Keywords

Fractional Cattaneo equation Time fractional derivative Local discontinuous Galerkin method Stability 

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Notes

Acknowledgments

This work is supported by the High-Level Personal Foundation of Henan University of Technology (2013BS041), Plan For Scientific Innovation Talent of Henan University of Technology (2013CXRC12), and the National Natural Science Foundation of China (11461072, 11426090), Foundation of Henan Educational Committee (15A110018), and China Postdoctoral Science Foundation funded project (2015M572115).

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.College of ScienceHenan University of TechnologyZhengzhouChina

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