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arXiv · 1507.07657

Finite difference/local discontinuous Galerkin method for solving the fractional diffusion-wave equation

Leilei Wei
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Abstract

In this paper a finite difference/local discontinuous Galerkin method for the fractional diffusion-wave equation is presented and analyzed. We first propose a new finite difference method to approximate the time fractional derivatives, and give a semidiscrete scheme in time with the truncation error $O((\Delta t)^2)$, where $\Delta t$ is the time step size. Further we develop a fully discrete scheme for the fractional diffusion-wave equation, and prove that the method is unconditionally stable and convergent with order $O(h^{k+1}+(\Delta t)^{2})$, where $k$ is the degree of piecewise polynomial. Extensive numerical examples are carried out to confirm the theoretical convergence rates.

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Leilei Wei. 2015-07-28. Finite difference/local discontinuous Galerkin method for solving the fractional diffusion-wave equation. https://arxiv.org/abs/1507.07657

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