## RODES

 swMATH ID: 30194 Software Authors: Tucker, Warwick Description: A rigorous ODE solver and Smale’s 14th problem: 5. The RODES Program: The RODES (Rigorous ODE Solver) program is a highly adaptive, multiprocessorprogram. As we pointed out earlier, the computations are performed in intervalarithmetic with directed rounding when necessary. This functionality is providedby the PROFIL/BIAS package (see [8]) which is supported on all architecturesutilized in the proof. The program was executed on 20 machines working in parallel.Data was passed between the processes via a common text file. All floating pointnumbers were passed with 17 digits of precision, which converts exactly according o the IEEE standard. The computers employed for the task were a variety ofSUN Sparc stations, with models ranging from LX, Sparc 4 to Ultra 1. The totalcomputational time in this setting was about 100 hours. Other setups with fewercomputers equipped with stronger processors have been performed with similarresults. In the sections to come, we will give an overview of the program’s globalstructure and the computations carried out. Homepage: https://link.springer.com/content/pdf/10.1007%2Fs002080010018.pdf Keywords: ODE solver; interval arithmetic; Lorenz equation; normal form; strange attractor Related Software: CAPD; Taylor; INTLAB; kepler98; TIDES; Matlab; MPFR; ATOMFT; ValEncIA-IVP; CkAnalytic; Chebfun; Cosy; Lifting; Transfer; Isabelle/HOL; DAETS; C-XSC; CAPD DynSys; VNODE; GitHub Cited in: 129 Publications

### Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
A rigorous ODE solver and Smale’s 14th problem. Zbl 1047.37012
Tucker, Warwick
2002
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### Cited by 202 Authors

 8 Barrio, Roberto 8 Lessard, Jean-Philippe 8 Tucker, Warwick 5 Araújo, Vítor 5 Melbourne, Ian 5 Mireles-James, Jason D. 5 Turaev, Dmitry V. 5 van den Berg, Jan Bouwe 5 Wilczak, Daniel 5 Zgliczyński, Piotr 3 Immler, Fabian 3 Pacifico, Maria José 3 Serrano, Sergio E. 2 Al-Mdallal, Qasem M. 2 Capinski, Maciej J. 2 Franco, Nuno 2 Gianfelice, Michele 2 Gonchenko, Sergey V. 2 Graça, Daniel Silva 2 Jaquette, Jonathan 2 Johnson, Tomas 2 Kalies, William D. 2 Kazakov, Alexey O. 2 Kiriki, Shin 2 Kuznetsov, Sergey P. 2 Li, Dongchen 2 Pchelintsev, Alexander Nikolaevich 2 Rodríguez, Marcos 2 Sanjurjo, José M. R. 2 Shen, Bo-Wen 2 Soma, Teruhiko 2 Srzednicki, Roman 2 Traut, Christoph 2 Vaienti, Sandro 2 Varandas, Paulo 2 Zhang, Xu 2 Zhong, Ning 1 Abad, Alberto J. 1 Aihara, Kazuyuki 1 Akhmedov, Odiljon S. 1 Al Sakkaf, Laila Y. 1 Allen, Mark G. 1 Araya, Ignacio J. 1 Aytaç, Hale 1 Azamov, Abdulla Azamovich 1 Bahsoun, Wael 1 Bailey, David Harold 1 Balázs, István 1 Bálint, Péter 1 Barge Yáñez, Héctor 1 Barker, Blake 1 Barreto, Guilherme A. 1 Bartha, Ferenc Ágoston 1 Beck, Margaret 1 Beskos, Alexandros 1 Birman, Joan S. 1 Björnsson, Jóhann 1 Blesa, Fernando 1 Bonomo, Wescley 1 Borwein, Jonathan Michael 1 Breden, Maxime 1 Butterley, Oliver 1 Castelli, Roberto 1 Coomes, Brian A. 1 Costa Filho, José T. 1 Courtois, Julien 1 Crisan, Dan O. 1 Dawes, Jonathan H. P. 1 Debnath, Lokenath 1 Dehornoy, Pierre 1 Dena, Ángeles 1 Deng, Bo 1 Doering, Charles Rogers 1 Duchesne, Gabriel William 1 Dudás, János 1 Dzetkulič, Tomáš 1 Evstigneev, Nikolai M. 1 Eyink, Gregory L. 1 Façanha, Tiago S. 1 Fang, Wei 1 Fiedler, Bernold 1 Fleurantin, Emmanuel 1 Fogelklou, Oswald 1 Fu, Yuli 1 Fuchs, Erich 1 Galias, Zbigniew 1 Garab, Ábel 1 Gardiner, Jason 1 Ghys, Étienne 1 Giesl, Peter 1 Giles, Michael B. 1 Gómez-Serrano, Javier 1 Gonchenko, Aleksandr Sergeevich 1 Grigor’ev, Dmitriĭ Yur’evich 1 Groothedde, C. M. 1 Groothedde, Chris 1 Gruber, Thiemo 1 Hafstein, Sigurður Freyr 1 Han, Qianqian 1 Hart, Allen G. ...and 102 more Authors
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### Cited in 62 Serials

 11 Physica D 6 Nonlinearity 5 Communications in Mathematical Physics 5 Journal of Statistical Physics 5 Journal of Differential Equations 5 Discrete and Continuous Dynamical Systems 5 Communications in Nonlinear Science and Numerical Simulation 4 Journal of Dynamics and Differential Equations 4 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 4 SIAM Journal on Applied Dynamical Systems 4 Journal of Computational Dynamics 3 Applied Mathematics and Computation 3 Transactions of the American Mathematical Society 3 Chaos 3 Regular and Chaotic Dynamics 3 Foundations of Computational Mathematics 2 Physics Letters. A 2 Chaos, Solitons and Fractals 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Journal of Automated Reasoning 2 Constraints 2 Annales Henri Poincaré 1 Advances in Applied Probability 1 Computer Physics Communications 1 Advances in Mathematics 1 BIT 1 Mathematische Zeitschrift 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Numerische Mathematik 1 Studies in Applied Mathematics 1 Topology and its Applications 1 Circuits, Systems, and Signal Processing 1 Numerical Algorithms 1 Pattern Recognition 1 SIAM Journal on Mathematical Analysis 1 Journal of Knot Theory and its Ramifications 1 New Zealand Journal of Mathematics 1 Journal of Nonlinear Science 1 Journal of Mathematical Sciences (New York) 1 Complexity 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Journal of Dynamical and Control Systems 1 Annales Mathematicae Silesianae 1 Qualitative Theory of Dynamical Systems 1 International Journal of Nonlinear Sciences and Numerical Simulation 1 Differential Equations 1 Differentsial’nye Uravneniya i Protsessy Upravleniya 1 Discrete and Continuous Dynamical Systems. Series B 1 Portugaliae Mathematica. Nova Série 1 Science in China. Series F 1 Logical Methods in Computer Science 1 Journal of Topology 1 Japanese Journal of Mathematics. 3rd Series 1 Studies in History and Philosophy of Science. Part B. Studies in History and Philosophy of Modern Physics 1 International Journal of Differential Equations 1 S$$\vec{\text{e}}$$MA Journal 1 Mathematics 1 SIAM/ASA Journal on Uncertainty Quantification 1 International Journal of Applied and Computational Mathematics 1 Nelineĭnaya Dinamika 1 Winter Braids Lecture Notes 1 Ural Mathematical Journal
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### Cited in 34 Fields

 82 Dynamical systems and ergodic theory (37-XX) 47 Ordinary differential equations (34-XX) 45 Numerical analysis (65-XX) 18 Partial differential equations (35-XX) 10 Computer science (68-XX) 9 Probability theory and stochastic processes (60-XX) 7 Biology and other natural sciences (92-XX) 7 Systems theory; control (93-XX) 6 Manifolds and cell complexes (57-XX) 5 Mechanics of particles and systems (70-XX) 4 Mathematical logic and foundations (03-XX) 4 Fluid mechanics (76-XX) 3 History and biography (01-XX) 3 Statistics (62-XX) 3 Geophysics (86-XX) 3 Operations research, mathematical programming (90-XX) 2 Approximations and expansions (41-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Operator theory (47-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Mechanics of deformable solids (74-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Information and communication theory, circuits (94-XX) 1 Combinatorics (05-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Group theory and generalizations (20-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Difference and functional equations (39-XX) 1 Integral transforms, operational calculus (44-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Classical thermodynamics, heat transfer (80-XX)