RODAS swMATH ID: 4112 Software Authors: E. Hairer, G. Wanner Description: Rosenbrock method of order 4(3), for problems of the form My’=f(x,y) with possibly singular matrix M; with dense output; algebraic order conditions are considered Concerning the linear algebra routines the user has the choice to link the code with DC_DECSOL and DECSOL or with DC_LAPACK and LAPACK and LAPACKC (actually, the file LAPACKC and the routines of DC_LAPACK which need COMPLEX*16 are not used) Homepage: http://www.unige.ch/~hairer/software.html Programming Languages: Fortran 77, C++, Matlab Keywords: Rosenbrock method; ordinary differential equation; ODE solver Related Software: Matlab; Ode15s; MEBDF; MATLAB ODE suite; ode23; ode23s; ode113; ode45; DASSL; VODE; RKC; RADAU; Mathematica; SUNDIALS; PETSc; GitHub; Expokit; ROS3P; S-ROCK; ODEPACK Referenced in: 1,741 Publications all top 5 Referenced by 2,174 Authors 34 Jackiewicz, Zdzislaw 28 Sandu, Adrian 23 D’Ambrosio, Raffaele 23 Kulikov, Gennady Yur’evich 22 Lubich, Christian 18 Akrivis, Georgios D. 18 Hairer, Ernst 17 González-Pinto, Severiano 17 Ostermann, Alexander 17 Weiner, Rüdiger 17 Zhang, Chengjian 16 Xiao, Aiguo 15 Abdi, Ali 15 Hundsdorfer, Willem H. 15 Paternoster, Beatrice 15 Rogov, Boris V. 14 Li, Shoufu 14 Wang, Wansheng 14 Zlatev, Zahari 13 Arnold, Martin 13 Brugnano, Luigi 13 Hernandez-Abreu, Domingo 13 Hojjati, Gholamreza 13 Mehrmann, Volker 13 Russo, Giovanni 13 Sommeijer, Ben P. 13 van der Houwen, Pieter J. 12 Boscarino, Sebastiano 12 Guglielmi, Nicola 12 Luk’yanenko, Dmitriĭ Vital’evich 12 Verwer, Jan G. 11 Butcher, John C. 11 Izzo, Giuseppe 10 Abdulle, Assyr 10 Gan, Siqing 10 Lang, Jens 10 Li, Buyang 10 Martín-Vaquero, Jesús 10 Minion, Michael L. 10 Pérez Rodríguez, S. 10 Rang, Joachim 10 Söderlind, Gustaf 10 Tian, Hongjiong 10 Zhao, Jingjun 9 Bulatov, Mikhail Valer’yanovich 9 Conte, Dajana 9 Jay, Laurent-Olivier 9 Pulch, Roland 8 Cash, Jeff R. 8 Christlieb, Andrew J. 8 de Swart, Jacques J. B. 8 Günther, Michael 8 Higueras, Inmaculada 8 Kovács, Balázs 8 Linh, Vu Hoang 8 Liu, Mingzhu 8 Montijano, Juan Ignacio 8 Vilmart, Gilles 8 Xu, Yang 7 Auzinger, Winfried 7 Bassi, Francesco 7 Chan, Robert Peng Kong 7 Chartier, Philippe 7 Faragó, István 7 Havasi, Ágnes 7 Khaliq, Abdul Q. M. 7 Kim, Philsu 7 Luan, Vu Thai 7 Magherini, Cecilia 7 Mazzia, Francesca 7 Tranquilli, Paul 7 Vermeire, Brian C. 7 Wanner, Gerhard 6 Alonso-Mallo, Isaías 6 Bartel, Andreas 6 Bayram, Mustafa 6 Bottasso, Carlo L. 6 Braś, Michał 6 Bu, Sunyoung 6 Burrage, Kevin 6 Cardone, Angelamaria 6 Carpenter, Mark H. 6 Chikitkin, A. V. 6 Gerdts, Matthias 6 Hauck, Cory D. 6 Iavernaro, Felice 6 Kalitkin, Nikolaĭ Nikolaevich 6 Kauthen, Jean-Paul 6 Kennedy, Christopher A. 6 López-Fernández, María 6 Luo, Xinlong 6 Novikov, Evgeniĭ Aleksandrovich 6 Pareschi, Lorenzo 6 Raha, Soumyendu 6 Ramos, Higinio 6 Riaza, Ricardo 6 Shampine, Lawrence Fred 6 Skvortsov, L. M. 6 Solovarova, Lyubov’ Stepanovna 6 Spijker, Marc N. ...and 2,074 more Authors all top 5 Referenced in 236 Serials 202 Applied Numerical Mathematics 201 Journal of Computational and Applied Mathematics 140 Journal of Computational Physics 73 Applied Mathematics and Computation 67 BIT 58 Computer Methods in Applied Mechanics and Engineering 54 Journal of Scientific Computing 50 Computers & Mathematics with Applications 49 Numerical Algorithms 39 Mathematics and Computers in Simulation 38 SIAM Journal on Scientific Computing 33 Mathematics of Computation 33 Numerische Mathematik 27 SIAM Journal on Numerical Analysis 26 Multibody System Dynamics 20 Computational Mathematics and Mathematical Physics 18 Computers and Fluids 16 Communications in Nonlinear Science and Numerical Simulation 15 Doklady Mathematics 13 Computational and Applied Mathematics 12 Computing 12 Applied Mathematics Letters 12 Mathematical and Computer Modelling 12 Journal of Mathematical Chemistry 12 Nonlinear Dynamics 11 Calcolo 11 Applied Mathematical Modelling 10 Celestial Mechanics and Dynamical Astronomy 9 International Journal of Computer Mathematics 9 Advances in Computational Mathematics 9 Journal of Applied Mathematics and Computing 9 Advances in Difference Equations 8 Journal of Mathematical Analysis and Applications 7 Computer Physics Communications 7 Journal of Dynamics and Differential Equations 7 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 6 Physica D 6 Computational Mechanics 6 Abstract and Applied Analysis 6 Foundations of Computational Mathematics 6 Discrete and Continuous Dynamical Systems. 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Mathematics of Control, Signals, and Systems 3 Japan Journal of Industrial and Applied Mathematics 3 Cybernetics and Systems Analysis 3 Computational Optimization and Applications 3 Journal of Mathematical Sciences (New York) 3 ETNA. Electronic Transactions on Numerical Analysis 3 Computing and Visualization in Science 3 Vietnam Journal of Mathematics 3 Discrete Dynamics in Nature and Society 3 Optimization and Engineering 3 Nonlinear Analysis. Real World Applications 3 Discrete and Continuous Dynamical Systems. Series B 3 Computational Methods in Applied Mathematics 3 Journal of Applied Mathematics 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Journal of Numerical Mathematics 3 International Journal of Numerical Analysis and Modeling 3 Springer Series in Computational Mathematics 3 Advances in Applied Mathematics and Mechanics 3 Afrika Matematika 2 Acta Mechanica 2 Discrete Applied Mathematics 2 Wave Motion 2 Chaos, Solitons and Fractals 2 Acta Mathematica Vietnamica 2 Journal of Multivariate Analysis 2 Kyungpook Mathematical Journal 2 Bulletin of the Iranian Mathematical Society 2 Journal of the Nigerian Mathematical Society 2 Computational Mathematics and Modeling 2 The Annals of Applied Probability 2 European Journal of Operational Research 2 Journal of Elasticity 2 SIAM Review 2 Archive of Applied Mechanics 2 Russian Mathematics 2 Journal of Inverse and Ill-Posed Problems ...and 136 more Serials all top 5 Referenced in 43 Fields 1,427 Numerical analysis (65-XX) 571 Ordinary differential equations (34-XX) 348 Partial differential equations (35-XX) 189 Fluid mechanics (76-XX) 101 Mechanics of particles and systems (70-XX) 81 Probability theory and stochastic processes (60-XX) 80 Biology and other natural sciences (92-XX) 73 Dynamical systems and ergodic theory (37-XX) 72 Mechanics of deformable solids (74-XX) 57 Systems theory; control (93-XX) 55 Classical thermodynamics, heat transfer (80-XX) 42 Calculus of variations and optimal control; optimization (49-XX) 41 Integral equations (45-XX) 32 Computer science (68-XX) 29 Optics, electromagnetic theory (78-XX) 27 Operations research, mathematical programming (90-XX) 21 Statistical mechanics, structure of matter (82-XX) 20 Geophysics (86-XX) 19 Linear and multilinear algebra; matrix theory (15-XX) 19 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 16 Operator theory (47-XX) 16 Information and communication theory, circuits (94-XX) 15 Approximations and expansions (41-XX) 13 Real functions (26-XX) 12 Quantum theory (81-XX) 11 Statistics (62-XX) 9 History and biography (01-XX) 9 Difference and functional equations (39-XX) 7 Relativity and gravitational theory (83-XX) 6 Integral transforms, operational calculus (44-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Functional analysis (46-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 Combinatorics (05-XX) 3 Differential geometry (53-XX) 2 General and overarching topics; collections (00-XX) 2 Special functions (33-XX) 2 Astronomy and astrophysics (85-XX) 1 Nonassociative rings and algebras (17-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Convex and discrete geometry (52-XX) Referencing Publications by Year