X-PLOR makes use of a third-order
finite difference approximation in dt
(Brünger, Brooks, and Karplus 1984).
First, the initial coordinates 
are subjected to the SHAKE method.
Then the system gets the initial velocities 
. Next,
the program prints the energy of the initial coordinates. A two-step
method is used to obtain the coordinates 
:
IF SHAKE constraints are present,
the SHAKE method is applied to 
with respect to 
.
Iteration from step n to step n+1 causes
.
The algorithm computes the forces 
.
The algorithm then computes
If required, the SHAKE method
is applied to 
with 
as the
reference set. Finally, the velocities at this step are computed:
(The velocities do not enter the equations to compute the
trajectory 
.) In case of
zero friction coefficients 
, this algorithm
reduces to the three-step Verlet method
(Verlet 1967).