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.

翻译：稳定化方法（又称切比雪夫方法）是沿负实轴具有扩展稳定域的显式方法，主要适用于源自抛物型偏微分方程的大型病态问题。本文提出显式两步龙格-库塔方法，其稳定性区间相比单步方法提高了2.5倍。同时，我们通过数值实验验证了该方法的精度与稳定性。