A SURVEY OF MULTIDERIVATIVE MULTISTEP INTEGRATORS

A full survey of multiderivative, multistep integrators has been carri ed out, including higher-order derivatives of the conventional force f unction (acceleration) in the equation(s) of motion. Their stability i ntervals along the imaginary axis and the negative part of the real ax is were explored. Most of them have strikingly high precision and some subgroups of these integrators are attractive because of their robust stability, as well as their efficiency. Among them, those using the h ighest-order derivatives only are the most stable members. Numerical e xperiments have shown that several of them are competitive in problems such as the restricted three-body problem. An algorithm is available to derive the formula for any specified integrator in this catalog. (C ) 1996 American Astronomical Society.