## Taylor

 swMATH ID: 10816 Software Authors: Jorba, Àngel; Zou, Maorong Description: 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. Homepage: http://www.maia.ub.edu/~angel/taylor/ Keywords: numerical examples; automatic differentiation; software; Taylor method; initial value problems; computer program; package; extended precision arithmetics Related Software: ATOMFT; TIDES; RODES; Mathematica; Cosy; MPFR; DAETS; CAPD; INTLAB; FADBAD++; Matlab; ADIFOR; ADOL-C; AUTO; mctoolbox; FFTW; RODAS; Taylor center; STDTST; NSDTST Cited in: 102 Publications
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### Cited by 160 Authors

 11 Mireles-James, Jason D. 10 Barrio, Roberto 8 Lessard, Jean-Philippe 6 Jorba, Àngel 5 Blesa, Fernando 5 Ollé, Mercè 4 Nguyen-Ba, Truong 4 Rodríguez, Marcos 4 Vaillancourt, Rémi 3 Abad, Alberto J. 3 Baeza, Antonio 3 Gimeno, Joan 3 Huguet, Gemma 3 Mulet, Pep 3 Naudot, Vincent 3 Nicolás, Begoña 3 Rodríguez, Oscar Córdoba 3 Simó, Carles 3 Soler, Jaume 3 Sterk, Alef E. 3 van den Berg, Jan Bouwe 3 Zorío, David 2 Al-Mdallal, Qasem M. 2 Boscarino, Sebastiano 2 Bozic, Vladan 2 Breden, Maxime 2 Broer, Henk W. 2 Burgos-García, Jaime 2 de la Llave, Rafael 2 Dijkstra, Henk A. 2 Erdelyi, Bela 2 Gómez, Gerard 2 Graça, Daniel Silva 2 Guillamon, Antoni 2 Leok, Melvin 2 Lu, Qiuying 2 Marzouk, Afnan Al 2 Masdemont, Josep J. 2 Nedialkov, Nedialko S. 2 Pérez-Palau, Daniel 2 Pryce, John D. 2 Russo, Giovanni 2 Schmitt, Jeremy M. 2 Vieiro, Arturo 2 Vitolo, Renato 1 Absil, Carlos Ortega 1 Al Sakkaf, Laila Y. 1 Alarcón, Tomás 1 Amodio, Pierluigi 1 Amore, Paolo 1 Bartha, Ferenc Ágoston 1 Bartuccelli, Michele V. 1 Batkhin, Alexandr B. 1 Belbruno, Edward A. 1 Belouettar, Salim 1 Bengochea, Abimael 1 Bervillier, Claude 1 Boudaoud, Hakim 1 Bürger, Raimund 1 Calleja, Renato C. 1 Castejón, Oriol 1 Castelli, Roberto 1 Castillo, Vanessa 1 Celletti, Alessandra 1 Charpentier, Isabelle 1 Churkina, Tatyana E. 1 Cyranka, Jacek 1 Deane, Jonathan H. B. 1 Dolgakov, I. 1 Duruisseaux, Valentin 1 Franco-Pérez, Luis 1 Frauenfelder, Urs Adrian 1 Galeş, Cătălin Bogdan 1 Gentile, Guido 1 Ghosh, Amitabha 1 Giordano, Thierry 1 Gómez-Serrano, Javier 1 Gonzalez, Jose Luis 1 Goodrich, John W. 1 Groothedde, C. M. 1 Groothedde, Chris 1 Hagstrom, Thomas M. 1 Hao, Han 1 Hayden, Kevin 1 Hennes, Daniel 1 Hénot, Olivier 1 Hungria, Allan 1 Iavernaro, Felice 1 Izzo, Dario 1 Jorba-Cuscó, Marc 1 Kalies, William D. 1 Karouma, Abdulrahman 1 Kehlet, Benjamin 1 Kengne, Emmanuel 1 Kepley, Shane 1 Koutsawa, Yao 1 Lázaro, Jose Tomas 1 Lejeune, Arnaud 1 Li, Xiaoming 1 Liao, Shijun ...and 60 more Authors
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### Cited in 44 Serials

 14 Communications in Nonlinear Science and Numerical Simulation 7 Celestial Mechanics and Dynamical Astronomy 6 Applied Mathematics and Computation 5 Discrete and Continuous Dynamical Systems. Series B 5 SIAM Journal on Applied Dynamical Systems 4 Physica D 4 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 3 Computers and Fluids 3 Numerical Algorithms 3 Journal of Dynamics and Differential Equations 3 Indagationes Mathematicae. New Series 3 SIAM Journal on Scientific Computing 2 Computers & Mathematics with Applications 2 Mathematics of Computation 2 BIT 2 Journal of Computational and Applied Mathematics 2 Computational and Applied Mathematics 2 Discrete and Continuous Dynamical Systems 2 Regular and Chaotic Dynamics 1 American Mathematical Monthly 1 Journal of Mathematical Biology 1 Chaos, Solitons and Fractals 1 ACM Transactions on Mathematical Software 1 International Journal for Numerical Methods in Engineering 1 Journal of Differential Equations 1 Mathematics and Computers in Simulation 1 Mechanics Research Communications 1 Programming and Computer Software 1 Theoretical Computer Science 1 Applied Numerical Mathematics 1 Mathematical and Computer Modelling 1 Journal of Scientific Computing 1 Journal of Nonlinear Science 1 Experimental Mathematics 1 Journal of Mathematical Sciences (New York) 1 Electronic Journal of Differential Equations (EJDE) 1 Complexity 1 Chaos 1 JNAIAM. Journal of Numerical Analysis, Industrial and Applied Mathematics 1 International Journal of Differential Equations 1 S$$\vec{\text{e}}$$MA Journal 1 Journal of Computational Dynamics 1 Mathematics 1 AMM. Applied Mathematics and Mechanics. (English Edition)
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### Cited in 19 Fields

 60 Numerical analysis (65-XX) 44 Ordinary differential equations (34-XX) 38 Dynamical systems and ergodic theory (37-XX) 31 Mechanics of particles and systems (70-XX) 9 Partial differential equations (35-XX) 5 Computer science (68-XX) 4 Biology and other natural sciences (92-XX) 3 Approximations and expansions (41-XX) 3 Mechanics of deformable solids (74-XX) 2 Operator theory (47-XX) 2 Fluid mechanics (76-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Mathematical logic and foundations (03-XX) 1 Field theory and polynomials (12-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Sequences, series, summability (40-XX) 1 Operations research, mathematical programming (90-XX)