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. Liu, Jie; Cao, Lixiong; Jiang, Chao; Ni, Bingyu; Zhang, Dequan: Parallelotope-formed evidence theory model for quantifying uncertainties with correlation (2020)
  2. 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)
  3. Groza, Ghiocel; Razzaghi, Mohsen: Approximation of solutions of polynomial partial differential equations in two independent variables (2019)
  4. Mezzarobba, Marc: Truncation bounds for differentially finite series (2019)
  5. Al Khawaja, U.; Al-Mdallal, Qasem M.: Convergent power series of (\operatornamesech(x)) and solutions to nonlinear differential equations (2018)
  6. 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)
  7. Blanes, Sergio; Casas, Fernando: A concise introduction to geometric numerical integration (2016)
  8. 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)
  9. Linaro, Daniele; Storace, Marco: \textscBAL: a library for the \textitbrute-force analysis of dynamical systems (2016)
  10. Pouly, Amaury; Graça, Daniel S.: Computational complexity of solving polynomial differential equations over unbounded domains (2016)
  11. Wilczak, Daniel; Serrano, Sergio; Barrio, Roberto: Coexistence and dynamical connections between hyperchaos and chaos in the 4D Rössler system: a computer-assisted proof (2016)
  12. Abad, A.; Barrio, R.; Marco-Buzunariz, M.; Rodríguez, M.: Automatic implementation of the numerical Taylor series method: a \textscMathematicaand \textscSageapproach (2015)
  13. Barrio, Roberto; Dena, Angeles; Tucker, Warwick: A database of rigorous and high-precision periodic orbits of the Lorenz 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. Chang, Shih-Hsiang: New algorithms for Taylor coefficients of indefinite integrals and their applications (2014)
  17. Chang, Shih-Hsiang: Taylor series method for solving a class of nonlinear singular boundary value problems arising in applied science (2014)
  18. Groza, Ghiocel; Razzaghi, Mohsen: A Taylor series method for the solution of the linear initial-boundary-value problems for partial differential equations (2013)
  19. Abad, Alberto; Barrio, Roberto; Blesa, Fernando; Rodríguez, Marcos: Algorithm 924, TIDES, a Taylor series integrator for differential equations (2012)
  20. Bailey, D. H.; Barrio, R.; Borwein, J. M.: High-precision computation: mathematical physics and dynamics (2012)

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