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(dense or banded), the Newton iteration is a Modified Newton iteration, in that the Jacobian is fixed (and usually out of date).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.

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  1. Beardsell, Guillaume; Blanquart, Guillaume: A cost-effective semi-implicit method for the time integration of fully compressible reacting flows with stiff chemistry (2020)
  2. Di Pietro, Franco; Fernández, Joaquín; Migoni, Gustavo; Kofman, Ernesto: Mixed-mode state-time discretization in ODE numerical integration (2020)
  3. Müller, Christian; Diedam, Holger; Mrziglod, Thomas; Schuppert, Andreas: A neural network assisted Metropolis adjusted Langevin algorithm (2020)
  4. Chernyshenko, Alexey Y.; Danilov, A. A.; Vassilevski, Y. V.: Numerical simulations for cardiac electrophysiology problems (2019)
  5. Khetan, Jawahar; Barua, Dipak: Analysis of Fn14-NF-(\kappa)B signaling response dynamics using a mechanistic model (2019)
  6. Yang, Qi; Zhao, Peng; Ge, Haiwen: reactingfoam-SCI: an open source CFD platform for reacting flow simulation (2019)
  7. Müller, Christian; Weysser, Fabian; Mrziglod, Thomas; Schuppert, Andreas: Markov-chain Monte-Carlo methods and non-identifiabilities (2018)
  8. Bob Carpenter and Andrew Gelman and Matthew Hoffman and Daniel Lee and Ben Goodrich and Michael Betancourt and Marcus Brubaker and Jiqiang Guo and Peter Li and Allen Riddell: Stan: A Probabilistic Programming Language (2017) not zbMATH
  9. Einkemmer, Lukas; Tokman, Mayya; Loffeld, John: On the performance of exponential integrators for problems in magnetohydrodynamics (2017)
  10. Carrasco, Juan A.: Numerically stable methods for the computation of exit rates in Markov chains (2016)
  11. Einkemmer, Lukas: A resistive magnetohydrodynamics solver using modern C++ and the Boost library (2016)
  12. Einkemmer, Lukas; Ostermann, Alexander: Overcoming order reduction in diffusion-reaction splitting. II: Oblique boundary conditions (2016)
  13. Hansen, M. A.; Sutherland, J. C.: Pseudotransient continuation for combustion simulation with detailed reaction mechanisms (2016)
  14. Kublik, Richard A.; Chopp, David L.: A locally adaptive time stepping algorithm for the solution to reaction diffusion equations on branched structures (2016)
  15. Linaro, Daniele; Storace, Marco: \textscBAL: a library for the \textitbrute-force analysis of dynamical systems (2016)
  16. MacArt, Jonathan F.; Mueller, Michael E.: Semi-implicit iterative methods for low Mach number turbulent reacting flows: operator splitting versus approximate factorization (2016)
  17. O’Sullivan, Stephen: A class of high-order Runge-Kutta-Chebyshev stability polynomials (2015)
  18. Jalbert, Eric; Eberl, Hermann J.: Numerical computation of sharp travelling waves of a degenerate diffusion-reaction equation arising in biofilm modelling (2014)
  19. Loffeld, J.; Tokman, M.: Implementation of parallel adaptive-Krylov exponential solvers for stiff problems (2014)
  20. Lv, Yu; Ihme, Matthias: Discontinuous Galerkin method for multicomponent chemically reacting flows and combustion (2014)

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