Numerical integration of the N-body ring problem by recurrent power series

Escaping orbits in the N ‐body ring problem

“…We have performed the integration of the equations of motion of the -body problem by means of the RPS method, as this method is much more accurate than RK4, RKF and DOPRI5. 21 Moreover, RPS achieves the smallest computational time, compared with the other three methods. The Jacobi constant associated with the RPS solution of the equations of motion remained the same to 17 significant figures.…”

On the analysis of the fractal basins of escape in the N ‐body ring problem

“…In Figure 4 The critical values of the Jacobi constant, C e , can be determined by means of the approach described by Caranicolas and Vozikis. 24 As we are interested in examining the escape geometry of the system, we have adopted the values C = We have used the recurrent power series (RPS) method 25,26 in order to numerically integrate the equations of motion. For this numerical integration, we have set the precision to 𝜖 = 10 −23 , and the number of term series to 26, so that the Jacobi constant remains constant up to 17 decimal digits along the numerical solution to the problem.…”

On the use of surfaces of section in the N‐body ring problem

“…We have used the RPS method for the numerical integration . The precision of the method has been fixed to ϵ =10 −23 , and the number of term series to 26.…”

“…We have used the RPS method for the numerical integration. 23,24 The precision of the method has been fixed to = 10 −23 , and the number of term series to 26. With these parameters, the Jacobi constant C of the equations of motion remains the same to 17 significant figures along the numerical integration of the problem.…”