Families of high-order composition methods (Q1862227)

For the design of high-order composition methods for ordinary differential equations, a new rule of thumb is proposed. It is based on the idea of setting all the outer stages equal. In certain cases it is shown that this concept leads to optimal rules (in a sense precisely described); in other cases the rules are not far from the optimum. The implications of the concept are studied, and specific examples are given describing the apparently good quality of the rules constructed according to the ideas of the paper.