  We present the derivation of a novel third-order hydrodynamic evolution
equation for shear stress tensor from kinetic theory. Boltzmann equation with
relaxation time approximation for the collision term is solved iteratively
using Chapman-Enskog like expansion to obtain the nonequilibrium phase-space
distribution function. Subsequently, the evolution equation for shear stress
tensor is derived from its kinetic definition up-to third-order in gradients.
We quantify the significance of the new derivation within one-dimensional
scaling expansion and demonstrate that the results obtained using third-order
viscous equations derived here provides a very good approximation to the exact
solution of Boltzmann equation in relaxation time approximation. We also show
that the time evolution of pressure anisotropy obtained using our equations is
in better agreement with transport results when compared with an existing
third-order calculation based on the second-law of thermodynamics.
