On the stability of two-step Runge–Kutta methods

Construction of efficient explicit two-step Runge–Kutta (TSRK) methods for ordinarydifferential equations is discussed. By obtaining the stability matrix of thesemethods, we present an overview of stability properties of such methods with the orderp and stage order q = p. Some special conditions are then applied to obtain efficientmethods with a large region of absolute stability.

Keywords:

Two-step Runge–Kutta methods , Stability matrix , Stability region , Orderconditions