Derivation of symmetric composition constants for symmetric integrators

This work focuses on the derivation of composition methods for the numerical integration of ordinary differential equations, which give rise to very challenging optimization problems. Composition is a useful technique for constructing high order approximations whilst conserving certain geometric properties. We survey existing composition methods and describe results of an intensive numerical search for new methods. Details of the search procedure are given along with numerical examples which indicate that the new methods perform better than previously known methods. Some insight into the location of global minima for these problems is obtained as a result.