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

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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.

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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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  1. College of Science, Henan University of Technology, Zhengzhou, Henan, 450001, China

    Leilei Wei

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Wei, L. Analysis of a new finite difference/local discontinuous Galerkin method for the fractional Cattaneo equation. Numer Algor 77, 675–690 (2018). https://doi.org/10.1007/s11075-017-0334-9

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