Abstract
In this paper, we consider the numerical approximation for the fractional diffusion-wave equation. The main purpose of this paper is to solve and analyze this problem by introducing an implicit fully discrete local discontinuous Galerkin method. The method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space. By choosing the numerical fluxes carefully we prove that our scheme is unconditionally stable and get L 2 error estimates of \(O(h^{k+1}+(\Delta t)^{2}+(\Delta t)^{\frac {\alpha }{2}}h^{k+1})\). Finally numerical examples are performed to illustrate the efficiency and the accuracy of the method.
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This work is supported by the NSF of Xinjiang Uigur Autonomous Region(No. 2013211B12).
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Dai, H., Wei, L. & Zhang, X. Numerical algorithm based on an implicit fully discrete local discontinuous Galerkin method for the fractional diffusion-wave equation. Numer Algor 67, 845–862 (2014). https://doi.org/10.1007/s11075-014-9827-y
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DOI: https://doi.org/10.1007/s11075-014-9827-y