Increasing the real stability boundary of explicit methods (Q922646)

The paper proposes an extension to `classical' explicit Runge-Kutta methods. This extension results in an increased real stability boundary. As disadvantage of the new methods the fact may be noted, that the algorithm has changed from a one-step method into a multistep method. Methods of orders 1-4 are analyzed. For these methods the resulting stability boundary is found. Some numerical results of applications of these methods to parabolic partial differential equations are given.