  We review the entropy based derivation of third-order hydrodynamic equations
and compare their solutions in one-dimensional boost-invariant geometry with
calculations by the partonic cascade BAMPS. We demonstrate that Grad's
approximation, which underlies the derivation of both Israel-Stewart and
third-order equations, describes the transverse spectra from BAMPS with high
accuracy. At the same time solutions of third-order equations are much closer
to BAMPS results than solutions of Israel-Stewart equations. Introducing a
resummation scheme for all higher-oder corrections to one-dimensional
hydrodynamic equation we demonstrate the importance of higher-order terms if
the Knudsen number is large.
