A third order Runge-Kutta method based on a convex combination of Lehmer means

Abstract

In this paper we introduce a modification of the third order Runge-Kutta method based on a convex combination of Lehmer means. The error of this method is also presented. The stability of this method is similar to the stability of third order Runge-Kutta method based on arithmetic mean. We end the discussion with two numerical examples to justify the effectiveness of the method.