  Algorithmic regularization uses a transformation of the equations of motion
such that the leapfrog algorithm produces exact trajectories for two-body
motion as well as regular results in numerical integration of the motion of
strongly interacting few-body systems. That algorithm alone is not sufficiently
accurate and one must use the extrapolation method for improved precision. This
requires that the basic leapfrog algorithm be time-symmetric, which is not
directly possible in the case of velocity-dependent forces, but is usually
obtained with the help of the implicit midpoint method. Here we suggest an
alternative explicit algorithmic regularization algorithm which can handle
velocity-dependent forces. This is done with the help of a generalized midpoint
method to obtain the required time symmetry, thus eliminating the need for the
implicit midpoint method and allowing the use of extrapolation.
