Contrary to the implementation of multistep (or multivalue) methods based on Nordsieck technique, variable stepsize (VS) methods do not require updating the input quantities when the stepsize changes. In this paper, we study VS explicit general linear methods (GLMs) of the order p and stage order \(q=p\) . We derive explicit formulas for some coefficients of such methods as equivalent conditions for the order conditions. Moreover, we investigate the local discretization error of these methods and introduce a reliable local error estimator. A construction of a special class of the VS explicit GLMs is described and some examples of these methods up to order five are given. The efficiency of the proposed methods and the reliability of the introduced local error estimator are illustrated by providing the results of some numerical experiments.
