A fully discrete local discontinuous Galerkin method with the generalized numerical flux to solve the tempered fractional reaction-diffusion equation

The tempered fractional diffusion equation could be recognized as the generalization of classic that truncation effects are included in bounded domains. This paper focuses on designing high order fully discrete local discontinuous Galerkin (LDG) method based generalized alternating numerical fluxes for equation. From a practical point view, flux which is different from purely has broader range applications. We first design an efficient finite difference scheme to approximate derivatives and then LDG prove unconditionally stable convergent with \begin{document}$ O(h^{k+1}+\tau^{2-\alpha}) $\end{document} , where h, \tau k step size space, time degree piecewise polynomials, respectively. Finally experimets performed show effectiveness testify accuracy method.