Name
Abstract | ||
|---|---|---|
This work considers the gravitational N-body problem and introduces global time-renormalization functions that allow the efficient numerical integration with fixed time-steps. First, a lower bound of the radius of convergence of the solution to the original equations is derived, which suggests an appropriate time-renormalization. In the new fictitious time r, it is then proved that any solution exists for all tau is an element of R and that it is uniquely extended as a holomorphic function to a strip of fixed width. As a by-product, a global power series representation of the solutions of the N-body problem is obtained. Notably, our global time-renormalizations remain valid in the limit when one of the masses vanishes. Finally, numerical experiments show the efficiency of the new time-renormalization functions for the numerical integration of some N-body problems with close encounters. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1137/20M1314719 | SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS |
Keywords | DocType | Volume |
gravitational N-body problems, time-renormalization, blow-up transformation, global power series representation | Journal | 19 |
Issue | ISSN | Citations |
4 | 1536-0040 | 0 |
PageRank | References | Authors |
0.34 | 0 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mikel Antoñana | 1 | 0 | 0.34 |
| P. Chartier | 2 | 144 | 29.70 |
| J. Makazaga | 3 | 11 | 2.53 |
| Ander Murua | 4 | 0 | 0.34 |