Composition Methods for Dynamical Systems Separable into Three Parts

New families of fourth-order composition methods for the numerical integration of initial value problems defined by ordinary differential equations are proposed. They are designed when the problem can be separated into three parts in such a way that each part is explicitly solvable. The methods are obtained by applying different optimization criteria and preserve geometric properties of the continuous problem by construction. Different numerical examples exhibit their improved performance with respect to previous splitting methods in the literature.