article published yes Tomoyuki Miyaji author Pawel Pilarczyk author 3768D56A-F248-11E8-B48F-1D18A9856A87 Marcio Gameiro author Hiroshi Kokubu author Konstantin Mischaikow author HeEd department Persistent Homology - Images, Data and Maps project 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. © 2016 IMACS. Published by Elsevier B.V. All rights reserved. Elsevier2016 eng 00037844700000310.1016/j.apnum.2016.04.005 10734 - 47 Miyaji T, Pilarczyk P, Gameiro M, Kokubu H, Mischaikow K. A study of rigorous ODE integrators for multi scale set oriented computations. <i>Applied Numerical Mathematics</i>. 2016;107:34-47. doi:<a href="https://doi.org/10.1016/j.apnum.2016.04.005">10.1016/j.apnum.2016.04.005</a> T. Miyaji, P. Pilarczyk, M. Gameiro, H. Kokubu, and K. Mischaikow, “A study of rigorous ODE integrators for multi scale set oriented computations,” <i>Applied Numerical Mathematics</i>, vol. 107. Elsevier, pp. 34–47, 2016. Miyaji, Tomoyuki, et al. “A Study of Rigorous ODE Integrators for Multi Scale Set Oriented Computations.” <i>Applied Numerical Mathematics</i>, vol. 107, Elsevier, 2016, pp. 34–47, doi:<a href="https://doi.org/10.1016/j.apnum.2016.04.005">10.1016/j.apnum.2016.04.005</a>. Miyaji T, Pilarczyk P, Gameiro M, Kokubu H, Mischaikow K. 2016. A study of rigorous ODE integrators for multi scale set oriented computations. Applied Numerical Mathematics. 107, 34–47. Miyaji, Tomoyuki, Pawel Pilarczyk, Marcio Gameiro, Hiroshi Kokubu, and Konstantin Mischaikow. “A Study of Rigorous ODE Integrators for Multi Scale Set Oriented Computations.” <i>Applied Numerical Mathematics</i>. Elsevier, 2016. <a href="https://doi.org/10.1016/j.apnum.2016.04.005">https://doi.org/10.1016/j.apnum.2016.04.005</a>. T. Miyaji, P. Pilarczyk, M. Gameiro, H. Kokubu, K. Mischaikow, Applied Numerical Mathematics 107 (2016) 34–47. Miyaji, T., Pilarczyk, P., Gameiro, M., Kokubu, H., &#38; Mischaikow, K. (2016). A study of rigorous ODE integrators for multi scale set oriented computations. <i>Applied Numerical Mathematics</i>. Elsevier. <a href="https://doi.org/10.1016/j.apnum.2016.04.005">https://doi.org/10.1016/j.apnum.2016.04.005</a> 11492018-12-11T11:50:25Z2025-09-22T09:58:16Z