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New families of fourth-order composition methods for the numericalintegration of initial value problems defined by ordinary differentialequations are proposed. They are designed when the problem can be separatedinto three parts in such a way that each part is explicitly solvable. Themethods are obtained by applying different optimization criteria and preservegeometric properties of the continuous problem by construction. Differentnumerical examples exhibit their improved performance with respect to previoussplitting methods in the literature.

Composition Methods for Dynamical Systems Separable into Three Parts