Computational efficiency of ADER and RK schemes for discontinuous Galerkin method in case of 1D Hopf equation

This paper considers Discontinuous Galerkin schemes based on Legendre polynomials of degree $K=2, 3$. Schemes are written to solve the one-dimensional Hopf equation. Unsteady solution is acquired with ADER and Runge-Kutta algorithms. The high order of numerical approaches is affirmed. The ADER method computational efficiency is studied in comparison with traditional approach. Tests that are used are with an analytical solution (linear solution and running half-wave), and with Burgers turbulence. The result of this work can be used to speed up 3D DG-based algorithms.