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. Amore, Paolo: Computing the solutions of the van der Pol equation to arbitrary precision (2022)
  2. Burgos-García, Jaime; Bengochea, Abimael; Franco-Pérez, Luis: The spatial Hill four-body problem. I: An exploration of basic invariant sets (2022)
  3. Calleja, Renato; Celletti, Alessandra; Gimeno, Joan; de la Llave, Rafael: Efficient and accurate KAM tori construction for the dissipative spin-orbit problem using a map reduction (2022)
  4. Hénot, Olivier; Lessard, Jean-Philippe; Mireles James, J. D.: Parameterization of unstable manifolds for DDEs: formal series solutions and validated error bounds (2022)
  5. Ollé, M.; Rodríguez, Ó.; Soler, J.: Study of the ejection/collision orbits in the spatial RTBP using the McGehee regularization (2022)
  6. van den Berg, Jan Bouwe; Groothedde, Chris; Lessard, Jean-Philippe: A general method for computer-assisted proofs of periodic solutions in delay differential problems (2022)
  7. Duruisseaux, Valentin; Schmitt, Jeremy; Leok, Melvin: Adaptive Hamiltonian variational integrators and applications to symplectic accelerated optimization (2021)
  8. Graça, Daniel S.; Zhong, Ning: Computability of differential equations (2021)
  9. Jorba, Àngel; Nicolás, Begoña: Using invariant manifolds to capture an asteroid near the (L_3) point of the Earth-Moon bicircular model (2021)
  10. Naudot, Vincent; Kepley, Shane; Kalies, William D.: Complexity in a hybrid van der Pol system (2021)
  11. Ollé, Merce; Rodríguez, Oscar; Soler, Jaume: Transit regions and ejection/collision orbits in the RTBP (2021)
  12. Tatjer, Joan Carles; Vieiro, Arturo: Dynamics of the QR-flow for upper Hessenberg real matrices (2021)
  13. Baeza, Antonio; Bürger, Raimund; Martí, María del Carmen; Mulet, Pep; Zorío, David: On approximate implicit Taylor methods for ordinary differential equations (2020)
  14. Batkhin, A. B.: Bifurcations of periodic solutions of a Hamiltonian system with a discrete symmetry group (2020)
  15. Castejón, Oriol; Guillamon, Antoni: Phase-amplitude dynamics in terms of extended response functions: invariant curves and Arnold tongues (2020)
  16. Dolgakov, I.; Pavlov, D.: Landau: a language for dynamical systems with automatic differentiation (2020)
  17. Gimeno, Joan; Jorba, Àngel: Using automatic differentiation to compute periodic orbits of delay differential equations (2020)
  18. Jorba, Àngel; Jorba-Cuscó, Marc; Rosales, José J.: The vicinity of the Earth-Moon (L_1) point in the bicircular problem (2020)
  19. Jorba, Àngel; Nicolás, Begoña: Transport and invariant manifolds near (L_3) in the Earth-Moon bicircular model (2020)
  20. Ollé, M.; Rodríguez, O.; Soler, J.: Analytical and numerical results on families of (n)-ejection-collision orbits in the RTBP (2020)

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