A FAMILY OF SYMPLECTIC INTEGRATORS - STABILITY, ACCURACY, AND MOLECULAR-DYNAMICS APPLICATIONS

The following integration methods for special second-order ordinary di fferential equations are studied: leapfrog, implicit midpoint, trapezo id, Stormer-Verlet, and Cowell-Numerov. We show that all are members, or equivalent to members, of a one-parameter family of schemes. Some m ethods have more than one common form, and we discuss a systematic enu meration of these forms. We also present a stability and accuracy anal ysis based on the idea of ''modified equations'' and a proof of symple cticness. It follows that Cowell-Numerov and ''LIM2'' (a method propos ed by Zhang and Schlick) are symplectic. A different interpretation of the values used by these integrators leads to higher accuracy and bet ter energy conservation. Hence, we suggest that the straightforward an alysis of energy conservation is misleading.