Open AccessAlgorithmic regularization with velocity‐dependent forces
Author(s) -
Mikkola Seppo,
Merritt David
Publication year - 2006
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1111/j.1365-2966.2006.10854.x
Subject(s) - extrapolation , regularization (linguistics) , physics , algorithm , point (geometry) , transformation (genetics) , equations of motion , classical mechanics , mathematics , motion (physics) , mathematical analysis , computer science , geometry , artificial intelligence , biochemistry , chemistry , gene
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.