Beeman's algorithm

Beeman's algorithm is a numerical method for integrating ordinary differential equations of second order, most specifically Newton's equations of motion in which acceleration depends on position. It was designed so that molecular dynamics simulations could handle large numbers of particles. The direct, explicit variant was published by Schofield in 1973 as a personal communication from Beeman, and this is what is commonly meant by Beeman's method. It is a variant of the Verlet integration method: it yields identical positions but uses a different formula for the velocities. In 1976 Beeman also published a class of implicit predictor-corrector multistep methods, of which the familiar direct method is the third-order member.