Analysis of a new finite difference/local discontinuous Galerkin method for the fractional Cattaneo equation |
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Authors: | Leilei Wei |
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Institution: | 1.College of Science,Henan University of Technology,Zhengzhou,China |
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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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