A FAMILY OF SYMPLECTIC INTEGRATORS: STABILITY, ACCURACY, AND MOLECULAR
The following integration methods for special second-order ordinary differential
equations are studied: leapfrog, implicit midpoint, trapezoid, Störmer-Verlet,
and Cowell-Numerov. We show that all are members or or equivalent to members,
of one-parameter family of schemes. Some methods have more than one common
form, and we discuss a systematic enumeration of these forms. We also present
a stability and accuracy analysis based on the idea of "modified equations"
and a proof of symplecticness. It follows that Cowell-Numerov
and "LIM2" (a method proposed by Zhang and Schlick) are symplectic.
A different interpretation of the values used by these integrators leads
to higher accuracy and better energy conservation. Hence we suggest that
the straightforward analysis of energy conservation is misleading.
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