  This paper studies the two-stage fourth-order accurate time discretization
\cite{LI-DU:2016} and applies it to special relativistic hydrodynamical
equations. It is shown that new two-stage fourth-order accurate time
discretizations can be proposed. With the aid of the direct Eulerian GRP
(generalized Riemann problem) methods \cite{Yang-He-Tang:2011,Yang-Tang:2012}
and the analytical resolution of the local "quasi 1D" GRP, the two-stage
fourth-order accurate time discretizations are successfully implemented for the
1D and 2D special relativistic hydrodynamical equations. Several numerical
experiments demonstrate the performance and accuracy as well as robustness of
our schemes.
