| Full text | |
| Author(s): |
Miyaji, Tomoyuki
[1]
;
Pilarczyk, Pawel
[2]
;
Gameiro, Marcio
[3]
;
Kokubu, Hiroshi
[4]
;
Mischaikow, Konstantin
[5]
Total Authors: 5
|
| Affiliation: | [1] Meiji Univ, Meiji Inst Adv Study Math Sci, Nakano Ku, 4-21-1 Nakano, Tokyo 1648525 - Japan
[2] IST Austria, Campus 1, A-3400 Klosterneuburg - Austria
[3] Univ Sao Paulo, Inst Ciencias Matemat & Computacao, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil
[4] Kyoto Univ, Dept Math, Kyoto 6068502 - Japan
[5] Rutgers State Univ, Dept Math, Hill Ctr, Busch Campus, 110 Frelinghusen Rd, Piscataway, NJ 08854 - USA
Total Affiliations: 5
|
| Document type: | Journal article |
| Source: | APPLIED NUMERICAL MATHEMATICS; v. 107, p. 34-47, SEP 2016. |
| Web of Science Citations: | 5 |
| Abstract | |
We study the usefulness of two most prominent publicly available rigorous ODE integrators: one provided by the CAPD group (capd.ii.uj.edu.pl), the other based on the COSY Infinity project (cosyinfinity.org). Both integrators are capable of handling entire sets of initial conditions and provide tight rigorous outer enclosures of the images under a time-T map. We conduct extensive benchmark computations using the well-known Lorenz system, and compare the computation time against the final accuracy achieved. We also discuss the effect of a few technical parameters, such as the order of the numerical integration method, the value of T, and the phase space resolution. We conclude that COSY may provide more precise results due to its ability of avoiding the variable dependency problem. However, the overall cost of computations conducted using CAPD is typically lower, especially when intervals of parameters are involved. Moreover, access to COSY is limited (registration required) and the rigorous ODE integrators are not publicly available, while CAPD is an open, source free software project. Therefore, we recommend the latter integrator for this kind of computations. Nevertheless, proper choice of the various integration parameters turns out to be of even greater importance than the choice of the integrator itself. (C) 2016 IMACS. Published by Elsevier B.V. All rights reserved. (AU) | |
| FAPESP's process: | 10/00875-9 - Topological methods and rigorous numerics for bifurcations of dynamical systems |
| Grantee: | Marcio Fuzeto Gameiro |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 13/07460-7 - Rigorous computations for PDEs |
| Grantee: | Marcio Fuzeto Gameiro |
| Support Opportunities: | Regular Research Grants |