A software package for the numerical integration of ODEs by means of high-order Taylor methods. This paper revisits the Taylor method for the numerical integration of initial value problems of ordinary differential equations (ODEs). The main goal is to present a computer program that outputs a specific numerical integrator for a given set of ODEs. The generated code includes a function to compute the jet of derivatives of the solution up to a given order plus adaptive selection of order and step size at run time. The package provides support for several extended precision arithmetics, including user-defined types. par The authors discuss the performance of the resulting integrator in some examples, showing that it is very competitive in many situations. This is especially true for integrations that require extended precision arithmetic. The main drawback is that the Taylor method is an explicit method, so it has all the limitations of these kind of schemes. For instance, it is not suitable for stiff systems.

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  1. Castillo, Vanessa; Lázaro, J. Tomás; Sardanyés, Josep: Dynamics and bifurcations in a simple quasispecies model of tumorigenesis (2017)
  2. Gonzalez, J.L.; Mireles James, J.D.: High-order parameterization of stable/unstable manifolds for long periodic orbits of maps (2017)
  3. Kehlet, Benjamin; Logg, Anders: A posteriori error analysis of round-off errors in the numerical solution of ordinary differential equations (2017)
  4. Mireles James, J.D.; Murray, Maxime: Chebyshev-Taylor parameterization of stable/unstable manifolds for periodic orbits: implementation and applications (2017)
  5. Breden, Maxime; Lessard, Jean-Philippe; Mireles James, Jason D.: Computation of maximal local (un)stable manifold patches by the parameterization method (2016)
  6. Hungria, Allan; Lessard, Jean-Philippe; Mireles James, J.D.: Rigorous numerics for analytic solutions of differential equations: the radii polynomial approach (2016)
  7. Izzo, Dario; Hennes, Daniel; Simões, Luís F.; Märtens, Marcus: Designing complex interplanetary trajectories for the global trajectory optimization competitions (2016)
  8. Lu, Qiuying; Naudot, Vincent: Bifurcation complexity from orbit-flip homoclinic orbit of weak type (2016)
  9. Pouly, Amaury; Graça, Daniel S.: Computational complexity of solving polynomial differential equations over unbounded domains (2016)
  10. Sánchez-Taltavull, Daniel; Vieiro, Arturo; Alarcón, Tomás: Stochastic modelling of the eradication of the HIV-1 infection by stimulation of latently infected cells in patients under highly active anti-retroviral therapy (2016)
  11. Sterk, A.E.: Extreme amplitudes of a periodically forced Duffing oscillator (2016)
  12. van den Berg, J.B.; Mireles James, J.D.: Parameterization of slow-stable manifolds and their invariant vector bundles: theory and numerical implementation (2016)
  13. Bartuccelli, Michele V.; Deane, Jonathan H.B.; Gentile, Guido: The high-order Euler method and the spin-orbit model (2015)
  14. Stefanelli, Letizia; Locatelli, Ugo: Quasi-periodic motions in a special class of dynamical equations with dissipative effects: a pair of detection methods (2015)
  15. Bartha, Ferenc A.; Munthe-Kaas, Hans Z.: Computing of B-series by automatic differentiation (2014)
  16. Cyranka, Jacek: Efficient and generic algorithm for rigorous integration forward in time of dPDEs. I (2014)
  17. Luque, Alejandro; Villanueva, Jordi: Quasi-periodic frequency analysis using averaging-extrapolation methods (2014)
  18. Pellegrini, Etienne; Russell, Ryan P.; Vittaldev, Vivek: $F$ and $G$ Taylor series solutions to the Stark and Kepler problems with Sundman transformations (2014)
  19. Huguet, Gemma; de la Llave, Rafael: Computation of limit cycles and their isochrons: fast algorithms and their convergence (2013)
  20. Lejeune, Arnaud; Boudaoud, Hakim; Potier-Ferry, Michel; Charpentier, Isabelle; Zahrouni, Hamid: Automatic solver for non-linear partial differential equations with implicit local laws: application to unilateral contact (2013)

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