  A novel second order family of explicit stabilized Runge-Kutta-Chebyshev
methods for advection-diffusion-reaction equations is introduced. The new
methods outperform existing schemes for relatively high Peclet number due to
their favorable stability properties and explicitly available coefficients. The
construction of the new schemes is based on stabilization using second kind
Chebyshev polynomials first used in the construction of the stochastic
integrator SK-ROCK. An adaptive algorithm to implement the new scheme is
proposed. This algorithm is able to automatically select the suitable step
size, number of stages, and damping parameter at each integration step.
Numerical experiments that illustrate the efficiency of the new algorithm are
presented.
