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Predictor-corrector algorithm

  Predictor-corrector algorithms constitute another commonly used class of methods to integrate the equations of motion. Those more often used in molecular dynamics (see e.g. [12]) are due to Gear, and consists of three steps:
1.
Predictor. From the positions and their time derivatives up to a certain order q, all known at time t, one ``predicts'' the same quantities at time $t+\Delta t$ by means of a Taylor expansion. Among these quantities are, of course, accelerations $\bf a$.
2.
Force evaluation. The force is computed taking the gradient of the potential at the predicted positions. The resulting acceleration will be in general different from the ``predicted acceleration''. The difference between the two constitutes an ``error signal''.
3.
Corrector. This error signal is used to ``correct'' positions and their derivatives. All the corrections are proportional to the error signal, the coefficient of proportionality being a ``magic number'' determined to maximize the stability of the algorithm.

For more details the reader is referred to [3], §3.2, or [6], §4.4. A detailed comparison between the Verlet and the Gear scheme can be found in [19].


next up previous contents
Next: Running, measuring, analyzing Up: Time integration algorithm Previous: The Verlet algorithm
Furio Ercolessi
9/10/1997