Algorithmic regularization with velocity-dependent forces
Abstract
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.