Two multiderivate multistep (MDMS) integrators

A preliminary survey of multiderivative multistep integrators is carried out. It is found that all of them are much more accurate than the classical linear multistep methods, but most of them have poor stability. After parameter adjustment, two of them (called MDMS I and MDMS II by us) are competitive with or superior to the classical methods in some aspects, such as accuracy and stability. MDMS I behaves especially well in all the cases which have been studied.