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; Cosy; Mathematica; MPFR; DAETS; CAPD; INTLAB; FADBAD++; Matlab; AUTO; GitHub; RODAS; CkAnalytic; ADIFOR; ADOL-C; mctoolbox; FFTW; gmp Cited in: 121 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year A software package for the numerical integration of ODEs by means of high-order Taylor methods. Zbl 1108.65072Jorba, Àngel; Zou, Maorong 2005 all top 5 Cited by 183 Authors 15 Mireles-James, Jason D. 10 Barrio, Roberto 10 Jorba, Àngel 9 Lessard, Jean-Philippe 7 Gimeno, Joan 7 Ollé, Mercè 5 Blesa, Fernando 5 Rodríguez, Oscar Córdoba 4 Nguyen-Ba, Truong 4 Nicolás, Begoña 4 Rodríguez, Marcos 4 Soler, Jaume 4 Vaillancourt, Rémi 3 Abad, Alberto J. 3 Baeza, Antonio 3 Celletti, Alessandra 3 de la Llave, Rafael 3 Huguet, Gemma 3 Jorba-Cuscó, Marc 3 Mulet, Pep 3 Naudot, Vincent 3 Simó, Carles 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 Calleja, Renato C. 2 Dijkstra, Henk A. 2 Duarte, Gladston 2 Erdelyi, Bela 2 Gómez, Gerard 2 Graça, Daniel Silva 2 Guillamon, Antoni 2 Hénot, Olivier 2 Khawaja, U. Al 2 Leok, Melvin 2 Liao, Shijun 2 Lu, Qiuying 2 Marzouk, Afnan Al 2 Masdemont, Josep J. 2 Murray, Maxime 2 Nedialkov, Nedialko S. 2 Pérez-Palau, Daniel 2 Pryce, John D. 2 Russo, Giovanni 2 Schmitt, Jeremy M. 2 M-Seara, Tere 2 Vieiro, Arturo 2 Vitolo, Renato 2 Zou, Maorong 1 Absil, Carlos Ortega 1 Al Sakkaf, Laila Y. 1 Alarcón, Tomás 1 Alomari, Mohammad Wajeeh 1 Amodio, Pierluigi 1 Amore, Paolo 1 Barrabés, Esther 1 Bartha, Ferenc Ágoston 1 Bartuccelli, Michele V. 1 Batiha, Iqbal M. 1 Batkhin, Alexandr B. 1 Belbruno, Edward A. 1 Belouettar, Salim 1 Bengochea, Abimael 1 Bervillier, Claude 1 Boudaoud, Hakim 1 Bürger, Raimund 1 Casas, Pablo S. 1 Castejón, Oriol 1 Castelli, Roberto 1 Castillo, Vanessa 1 Charpentier, Isabelle 1 Churkina, Tatyana E. 1 Cyranka, Jacek 1 Deane, Jonathan H. B. 1 Dolgakov, I. 1 Drubi, Fátima 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 González, Jorge A. 1 Gonzalez, Jose Luis 1 Goodrich, John W. 1 Gözükirmizi, Coşar 1 Groothedde, C. M. 1 Groothedde, Chris 1 Hagstrom, Thomas M. 1 Hao, Han 1 Hayden, Kevin 1 Hennes, Daniel ...and 83 more Authors all top 5 Cited in 48 Serials 15 Communications in Nonlinear Science and Numerical Simulation 10 Celestial Mechanics and Dynamical Astronomy 7 Applied Mathematics and Computation 6 Discrete and Continuous Dynamical Systems. Series B 6 SIAM Journal on Applied Dynamical Systems 5 Physica D 4 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 4 Journal of Nonlinear Science 3 Computers and Fluids 3 Numerical Algorithms 3 Journal of Dynamics and Differential Equations 3 Indagationes Mathematicae. 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Journal of Numerical Analysis, Industrial and Applied Mathematics 1 International Journal of Differential Equations 1 Advances in Applied Mathematics and Mechanics 1 S\(\vec{\text{e}}\)MA Journal 1 Journal of Computational Dynamics 1 Mathematics 1 AMM. Applied Mathematics and Mechanics. (English Edition) 1 SN Partial Differential Equations and Applications all top 5 Cited in 21 Fields 67 Numerical analysis (65-XX) 46 Ordinary differential equations (34-XX) 42 Dynamical systems and ergodic theory (37-XX) 42 Mechanics of particles and systems (70-XX) 10 Partial differential equations (35-XX) 5 Computer science (68-XX) 4 Biology and other natural sciences (92-XX) 3 Approximations and expansions (41-XX) 2 Operator theory (47-XX) 2 Mechanics of deformable solids (74-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 Optics, electromagnetic theory (78-XX) 1 Quantum theory (81-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year