Algebraic analysis approach for multibody problems 2

The algebraic model (ALG) proposed by the authors has sufficiently high accuracy in calculating the motion of a test particle with all the field particles at rest. When all the field particles are moving, however, the ALG has relatively poor prediction ability on the motion of the test particle initially at rest. None the less, the ALG approximation gives a good results for the statistical quantities, such a variance of velocity changes or the scattering cross section, for a sufficiently large number of Monte Carlo trials. For a 108-body problem, which corresponds to full three-dimensional Coulomb interactions within the Debye sphere in a fusion plasma, the ALG approximation is 263 times as fast as the 6-stage 5-th order Runge-Kutta-Fehlberg method with an absolute error tolerance of 10-16. (author)