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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.

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