# Beeman's algorithm

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**Beeman's algorithm** ^{[1]} is is a method for numerically integrating ordinary differential equations, generally position and velocity, which is closely related to Verlet integration.

where *x* is the position, *v* is the velocity, *a* is the acceleration, *t* is time, and is the time-step.

A predictor-corrector variant is useful when the forces are velocity-dependent:

The velocities at time are then calculated from the positions.

The accelerations at time are then calculated from the positions and predicted velocities.