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On error estimation in almost Runge-Kutta (ARK) methods

In Runge-Kutta Theory, it is common knowledge that the bounds for the local truncation errors do not form a suitable basis for monitoring the local truncation error [7]. In a number of literatures including [1], Richardson Extrapolation technique has been shown to be a very reliable means of obtaining error estimates for Runge-Kutta methods. In this paper, we have sought to investigate, by means of rigorous numerical experiments, if this effectiveness of Richardson extrapolation technique extends to ARK methods and our results show that it doesn’t.