Main Research interests The CAPD group Applications of the CAPD Download the library CAPD Documentation Related links
How to cite CAPD

Contact:
Division of Computational Mathematics
Jagiellonian University
Lojasiewicza 6
30-348 Krakow, Poland virtual:

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Study:

Computational Mathematics
@Jagiellonian University

The main reference to the CAPD library is the following article

T. Kapela, M. Mrozek, D. Wilczak, P. Zgliczynski,
CAPD::DynSys: a flexible C++ toolbox for rigorous numerical analysis of dynamical systems,
Communications in Nonlinear Science and Numerical Simulation, Volume 101, October 2021, 105578. https://doi.org/10.1016/j.cnsns.2020.105578

One may also consider to cite articles, where some of important algorithms implemented in the CAPD library have been developed.

• rigorous computation of Poincare maps:
  T. Kapela, D. Wilczak, P. Zgliczynski, Recent advances in rigorous computation of Poincare maps Communications in Nonlinear Science and Numerical Simulation, Volume 110, July 2022, 106366. https://doi.org/10.1016/j.cnsns.2022.106366
• rigorous integration of variational equations for ODEs (C¹ algorithms)
  P. Zgliczynski, C¹-Lohner algorithm, Foundations of Computational Mathematics, (2002) 2:429-465.
  
  I. Walawska, D. Wilczak, Validated numerics for period-tupling and touch-and-go bifurcations of symmetric periodic orbits in reversible systems Communications in Nonlinear Science and Numerical Simulation, Vol. 74C (2019), 30-54.
• rigorous integration of higher order variational equations for ODEs (C^r algorithm)
  D. Wilczak, P. Zgliczynski, C^r-Lohner algorithm, Schedae Informaticae, Vol. 20 (2011), 9-46.
• rigorous integration of differential inclusions
  T. Kapela, P. Zgliczynski, A Lohner-type algorithm for control systems and ordinarydifferential inclusions, Discrete and Continuous Dynamical Systems B, 11 (2009), 365-385.