CAPD

Software library that aims to provide a set of flexible C++ modules designed for rigorous numerics in dynamical systems. The CAPD library is a collection of flexible C++ modules which are mainly designed to computation of homology of sets and maps and nonrigorous and validated numerics for dynamical systems. It is distributed under the terms of GNU GPL license.


References in zbMATH (referenced in 52 articles )

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  1. Galias, Zbigniew; Tucker, Warwick: Rigorous integration of smooth vector fields around spiral saddles with an application to the cubic Chua’s attractor (2019)
  2. Sogokon, Andrew; Jackson, Paul B.; Johnson, Taylor T.: Verifying safety and persistence in hybrid systems using flowpipes and continuous invariants (2019)
  3. Balázs, István; van den Berg, Jan Bouwe; Courtois, Julien; Dudás, János; Lessard, Jean-Philippe; Vörös-Kiss, Anett; Williams, J. F.; Yin, Xi Yuan: Computer-assisted proofs for radially symmetric solutions of PDEs (2018)
  4. Kalies, William D.; Kasti, Dinesh; Vandervorst, Robert: An algorithmic approach to lattices and order in dynamics (2018)
  5. Rohou, Simon; Jaulin, Luc; Mihaylova, Lyudmila; Le Bars, Fabrice; Veres, Sandor M.: Reliable nonlinear state estimation involving time uncertainties (2018)
  6. Szczelina, Robert; Zgliczyński, Piotr: Algorithm for rigorous integration of delay differential equations and the computer-assisted proof of periodic orbits in the Mackey-Glass equation (2018)
  7. Villegas Pico, Hugo Nestor; Aliprantis, Dionysios C.: Reachability analysis of linear dynamic systems with constant, arbitrary, and Lipschitz continuous inputs (2018)
  8. Figueras, J.-Ll.; Haro, A.; Luque, A.: Rigorous computer-assisted application of KAM theory: a modern approach (2017)
  9. Galias, Zbigniew: Systematic search for wide periodic windows and bounds for the set of regular parameters for the quadratic map (2017)
  10. Gonzalez-Lorenzo, Aldo; Bac, Alexandra; Mari, Jean-Luc; Real, Pedro: Allowing cycles in discrete Morse theory (2017)
  11. Kapela, Tomasz; Simó, Carles: Rigorous KAM results around arbitrary periodic orbits for Hamiltonian systems (2017)
  12. Belova, Anna: Rigorous enclosures of rotation numbers by interval methods (2016)
  13. Czechowski, Aleksander; Zgliczyński, Piotr: Existence of periodic solutions of the Fitzhugh-Nagumo equations for an explicit range of the small parameter (2016)
  14. Gonzalez-Lorenzo, Aldo; Juda, Mateusz; Bac, Alexandra; Mari, Jean-Luc; Real, Pedro: Fast, simple and separable computation of Betti numbers on three-dimensional cubical complexes (2016)
  15. Haro, Àlex; Canadell, Marta; Figueras, Jordi-Lluís; Luque, Alejandro; Mondelo, Josep-Maria: The parameterization method for invariant manifolds. From rigorous results to effective computations (2016)
  16. Miyaji, Tomoyuki; Pilarczyk, Paweł; Gameiro, Marcio; Kokubu, Hiroshi; Mischaikow, Konstantin: A study of rigorous ODE integrators for multi-scale set-oriented computations (2016)
  17. van den Berg, Jan Bouwe; Mireles James, Jason D.; Reinhardt, Christian: Computing (un)stable manifolds with validated error bounds: non-resonant and resonant spectra (2016)
  18. Walawska, Irmina; Wilczak, Daniel: An implicit algorithm for validated enclosures of the solutions to variational equations for ODEs (2016)
  19. Weilandt, Frank; Mrozek, Marian; Mischaikow, Konstantin: Discretization strategies for computing Conley indices and Morse decompositions of flows (2016)
  20. Wilczak, Daniel; Serrano, Sergio; Barrio, Roberto: Coexistence and dynamical connections between hyperchaos and chaos in the 4D Rössler system: a computer-assisted proof (2016)

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