Second order stabilized two-step Runge–Kutta methods

Stabilized methods for the numerical solution of ODEs, also called Chebyshev methods, are explicit with extended stability domains along negative real axis. These intended large mildly stiff problems, originating mainly from parabolic PDEs. In this paper we present two-step Runge–Kutta–Chebyshev order two, which have more than 2.3 times larger intervals analogous one-step methods. Explicit formulae derived, as well an effective recurrent scheme calculation methods’ coefficients arbitrary number stages. Our experiments confirm accuracy and properties proposed show that at least in case constant time steps they can compete well-known ROCK2 method.