Algorithm 924: TIDES, a Taylor Series Integrator for Differential EquationS. We present a new free software called TIDES, based on the classical Taylor series method and using an optimized variable-stepsize variable-order formulation. This software, developed by A. Abad, R Barrio, F. Blesa, M. Rodriguez, (GME), consists on a library on C and FORTRAN and a precompiler done in MATHEMATICA that creates a C or a FORTRAN program that permits to compute up to any precision level (by using multiple precision libraries for high precision when needed) the solution of an ODE system. The software has been done to be extremely easy to use. The program also permits to compute in a direct way not only the solution of the differential system, but also the partial derivatives, up to any order, of the solution with respect to the initial conditions or any parameter of the system. This is based on the extended Taylor series method for sensitivity analysis.

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  1. Amore, Paolo: Computing the solutions of the van der Pol equation to arbitrary precision (2022)
  2. Graça, Daniel S.; Zhong, Ning: Computability of differential equations (2021)
  3. Serrano, Sergio; Martínez, M. Angeles; Barrio, Roberto: Order in chaos: structure of chaotic invariant sets of square-wave neuron models (2021)
  4. Baeza, Antonio; Bürger, Raimund; Martí, María del Carmen; Mulet, Pep; Zorío, David: On approximate implicit Taylor methods for ordinary differential equations (2020)
  5. Barrio, Roberto; Carvalho, Maria; Castro, Luísa; Rodrigues, Alexandre A. P.: Experimentally accessible orbits near a Bykov cycle (2020)
  6. Batkhin, A. B.: Bifurcations of periodic solutions of a Hamiltonian system with a discrete symmetry group (2020)
  7. Liu, Jie; Cao, Lixiong; Jiang, Chao; Ni, Bingyu; Zhang, Dequan: Parallelotope-formed evidence theory model for quantifying uncertainties with correlation (2020)
  8. Danieli, Carlo; Manda, Bertin Many; Mithun, Thudiyangal; Skokos, Charalampos: Computational efficiency of numerical integration methods for the tangent dynamics of many-body Hamiltonian systems in one and two spatial dimensions (2019)
  9. Groza, Ghiocel; Razzaghi, Mohsen: Approximation of solutions of polynomial partial differential equations in two independent variables (2019)
  10. Hernandez, Kevin; Elgohary, Tarek A.; Turner, James D.; Junkins, John L.: A novel analytic continuation power series solution for the perturbed two-body problem (2019)
  11. Mezzarobba, Marc: Truncation bounds for differentially finite series (2019)
  12. Al Khawaja, U.; Al-Mdallal, Qasem M.: Convergent power series of (\operatornamesech(x)) and solutions to nonlinear differential equations (2018)
  13. Al Sakkaf, Laila Y.; Al-Mdallal, Qasem M.; Al Khawaja, U.: A numerical algorithm for solving higher-order nonlinear BVPs with an application on fluid flow over a shrinking permeable infinite long cylinder (2018)
  14. Pérez-Palau, Daniel; Gómez, Gerard; Masdemont, Josep J.: A new subdivision algorithm for the flow propagation using polynomial algebras (2018)
  15. Amodio, P.; Iavernaro, F.; Mazzia, F.; Mukhametzhanov, M. S.; Sergeyev, Ya. D.: A generalized Taylor method of order three for the solution of initial value problems in standard and infinity floating-point arithmetic (2017)
  16. Blanes, Sergio; Casas, Fernando: A concise introduction to geometric numerical integration (2016)
  17. 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)
  18. Linaro, Daniele; Storace, Marco: \textscBAL: a library for the \textitbrute-force analysis of dynamical systems (2016)
  19. Pouly, Amaury; Graça, Daniel S.: Computational complexity of solving polynomial differential equations over unbounded domains (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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