Second order stabilized two-step Runge-Kutta methods

Abstract

Stabilized methods (also called Chebyshev methods) are explicit methods with extended stability domains along the negative real axis. These methods are intended for large mildly stiff problems, originating mainly from parabolic PDEs. In this paper we present explicit two-step Runge-Kutta methods, which have an increased stability interval in comparison with one-step methods (up to 2.5 times). Also, we perform some numerical experiments to confirm the accuracy and stability of this methods.