CVODE swMATH ID: 4947 Software Authors: Cohen, S.D., Hindmarsh, A.C. Description: CVODE is a solver for stiff and nonstiff ordinary differential equation (ODE) systems (initial value problem) given in explicit form y’ = f(t,y).The methods used in CVODE are variable-order, variable-step multistep methods. For nonstiff problems, CVODE includes the Adams-Moulton formulas, with the order varying between 1 and 12. For stiff problems, CVODE includes the Backward Differentiation Formulas (BDFs) in so-called fixed-leading coefficient form, with order varying between 1 and 5. For either choice of formula, the resulting nonlinear system is solved (approximately) at each integration step. For this, CVODE offers the choice of either functional iteration, suitable only for nonstiff systems, and various versions of Newton iteration. In the cases of a direct linear solver (dense or banded), the Newton iteration is a Modified Newton iteration, in that the Jacobian is fixed (and usually out of date). When using a Krylov method as the linear solver, the iteration is an Inexact Newton iteration, using the current Jacobian (through matrix-free products), in which the linear residual is nonzero but controlled.When used in conjunction with the serial NVECTOR module, CVODE provides both direct (dense and band) solvers and three preconditioned Krylov (iterative) solvers (GMRES, Bi-CGStab, and TFQMR). In the parallel version (CVODE used with a parallel NVECTOR module) only the Krylov linear solvers are available. An approximate diagonal Jacobian option is also available with both versions. For the serial version, there is a banded preconditioner module called CVBANDPRE for use with the Krylov solvers, while for the parallel version there is a preconditioner module called CVBBDPRE which provides a band-block-diagonal preconditioner.For use with Fortran applications, a set of Fortran/C interface routines, called FCVODE, is also supplied. These are written in C, but assume that the user calling program and all user-supplied routines are in Fortran. Homepage: https://computation.llnl.gov/casc/sundials/description/description.html#descr_cvode Related Software: SUNDIALS; RODAS; RKC; Cantera; VODE; Boost C++ Libraries; Boost; CHEMKIN; AUTO; Doxygen; DIFSUB; DRFM; PETSc; libMC; cppmhd; GRI-Mech 3.0; libMesh; XPPAUT; AUTO-07P; SWIG Cited in: 62 Publications all top 5 Cited by 134 Authors 4 Barton, Paul I. 4 Najm, Habib N. 4 Scott, Joseph K. 4 Shadid, John N. 3 Einkemmer, Lukas 3 Ray, Jaideep 3 Ropp, David L. 2 Boaretto, B. R. R. 2 Budzinski, R. C. 2 Chalupecký, Vladimír 2 Fernández, Joaquín L. 2 Hansen, Michael Alan 2 Hu, Heping 2 Kofman, Ernesto 2 Kurths, Jürgen 2 Loffeld, John 2 Mrziglod, Thomas 2 Muntean, Adrian 2 Ober, Curtis C. 2 Prado, T. L. 2 Safta, Cosmin 2 Schuppert, Andreas A. 2 Sutherland, James Clayton 2 Tian, Fuqiang 2 Tokman, Mayya 1 Abdelsamie, Abouelmagd 1 Abukhdeir, Nasser Mohieddin 1 Airini, Razvan 1 Allan, Benjamin A. 1 Alzahrani, H. H. 1 Amuzescu, Bogdan 1 Armstrong, Robert C. 1 Barua, Dipak 1 Beardsell, Guillaume 1 Beaudoin, Armand J. 1 Bidani, Akhil 1 Blanquart, Guillaume 1 Bratsos, Athanasios 1 Bridewell, Will 1 Brown, Peter N. 1 Brydon, David 1 Cadusch, Peter J. 1 Carrasco, Juan Antonio 1 Chernyshenko, Alexey Y. 1 Chopp, David L. 1 Ciottoli, Pietro Paolo 1 Colella, Phillip 1 Crunelli, Vincenzo 1 Dafilis, Mathew P. 1 Danilov, Alexander A. 1 Debusschere, Bert J. 1 Di Pietro, Franco 1 Diedam, Holger 1 Dorr, Milo R. 1 Drummond, L. Anthony 1 Džeroski, Sašo 1 Eberl, Hermann J. 1 Epureanu, Florin Bogdan 1 Errington, Adam C. 1 Fidler, Josef 1 Frascoli, Federico 1 Fressengeas, Claude 1 Frischmuth, Kurt 1 Frouzakis, Christos Emmanouil 1 Galassi, Riccardo Malpica 1 Gao, Long 1 Ge, Haiwen 1 Grant, Keith E. 1 Hamm, Thomas 1 Hänler, Michael 1 Heming, T. A. 1 Hindmarsh, Alan C. 1 Horváth, Dezső 1 Hughes, Stuart W. 1 Ihme, Matthias 1 Jalbert, Eric 1 Kashima, Kenji 1 Katsoulakis, Markos A. 1 Kennedy, Christopher A. 1 Khalil, Mohammad 1 Khetan, Jawahar 1 Knio, Omar M. 1 Knott, Thomas 1 Kublik, Richard A. 1 Langley, Pat 1 Lartigue, Ghislain 1 Lee, Pilhwa 1 Lee, Steven L. 1 Lefantzi, Sophia 1 Liley, David T. J. 1 Linaro, Daniele 1 Lv, Yu 1 MacArt, Jonathan F. 1 Mann, Stefan A. 1 Marder, Michael 1 Marques, Osni A. 1 Marzorati, Denise 1 Migoni, Gustavo 1 Mohan, Ananthan 1 Moore, Peter K. ...and 34 more Authors all top 5 Cited in 33 Serials 14 Journal of Computational Physics 4 Combustion Theory and Modelling 3 SIAM Journal on Scientific Computing 3 Journal of Theoretical Biology 2 Computers and Fluids 2 Computer Physics Communications 2 Physica A 2 ACM Transactions on Mathematical Software 2 Journal of Global Optimization 2 Monte Carlo Methods and Applications 1 Journal of Engineering Mathematics 1 Journal of the Mechanics and Physics of Solids 1 Mathematical Biosciences 1 Bulletin of Mathematical Biology 1 Applied Mathematics and Computation 1 Journal of Computational and Applied Mathematics 1 Journal of Optimization Theory and Applications 1 Mathematics and Computers in Simulation 1 Numerische Mathematik 1 Physica D 1 Applied Numerical Mathematics 1 Journal of Tsinghua University. Science and Technology 1 Machine Learning 1 Japan Journal of Industrial and Applied Mathematics 1 Numerical Algorithms 1 Advances in Computational Mathematics 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Communications in Nonlinear Science and Numerical Simulation 1 Methodology and Computing in Applied Probability 1 Progress in Computational Fluid Dynamics 1 COE Lecture Note 1 Science China. Technological Sciences all top 5 Cited in 17 Fields 37 Numerical analysis (65-XX) 21 Fluid mechanics (76-XX) 14 Biology and other natural sciences (92-XX) 9 Partial differential equations (35-XX) 8 Classical thermodynamics, heat transfer (80-XX) 7 Ordinary differential equations (34-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Systems theory; control (93-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Mechanics of deformable solids (74-XX) 2 Probability theory and stochastic processes (60-XX) 1 General and overarching topics; collections (00-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Optics, electromagnetic theory (78-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year