Algorithmic regularization with velocity-dependent forces

• Published in: Monthly notices of the Royal Astronomical Society Vol. 372; no. 1; pp. 219 - 223
• Main Authors: Mikkola, Seppo, Merritt, David
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 11.10.2006; Blackwell Science; Oxford University Press
• Subjects: Algorithms; Astronomy; Astrophysics; celestial mechanics; Earth, ocean, space; Exact sciences and technology; Linear equations; methods: N-body simulations; Stars & galaxies; stellar dynamics; stellar dynamics; celestial mechanics; body simulations; methods; methods: N-body simulations; Algorithms; Numerical integration; Digital simulation; N body system; Trajectories; Equations of motion; Regularization; Stellar dynamics; Celestial mechanics
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1111/j.1365-2966.2006.10854.x

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.