This paper focuses on providing the high order algorithms for the space–time tempered fractional diffusion-wave equation. The designed schemes are unconditionally stable and have the global truncation error   O(τ 2 +h 2 )     O   (    τ    2    +    h    2    )        , being theoretically proved and numerically verified.
['Minghua Chen', 'Weihua Deng']
A second-order accurate numerical method for the space-time tempered fractional diffusion-wave equation