Algorithmic regularization with velocity-dependent forces

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 mid-point 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 mid-point method to obtain the required time symmetry, thus eliminating the need for the implicit mid-point method and allowing the use of extrapolation.