CVODE, a stiff/nonstiff ODE solver in C

@article{Cohen1996CVODEAS,
  title={CVODE, a stiff/nonstiff ODE solver in C},
  author={Scott Cohen and Alan C. Hindmarsh},
  journal={Computers in Physics},
  year={1996},
  volume={10},
  pages={138-143}
}
CVODE is a package written in C for solving initial value problems for ordinary di erential equations. It provides the capabilities of two older Fortran packages, VODE and VODPK. CVODE solves both sti and nonsti systems, using variable-coe cient Adams and BDF methods. In the sti case, options for treating the Jacobian of the system include dense and band matrix solvers, and a preconditioned Krylov (iterative) solver. In the highly modular organization of CVODE, the core integrator module is… 

Figures from this paper

CVODES: The Sensitivity-Enabled ODE Solver in SUNDIALS
TLDR
The current capabilities of CVODES, its design principles, and its user interface are described, and an example problem is provided to illustrate the performance ofCVODES.
PVODE, an ODE Solver for Parallel Computers
TLDR
PVODE is a general-purpose solver for ordinary differential equation (ODE) systems that implements methods for both stiff and nonstiff systems that is written in ANSI standard C, with a highly modular structure.
SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers
TLDR
The current capabilities of the codes, along with some of the algorithms and heuristics used to achieve efficiency and robustness, are described.
PVODE and KINSOL: parallel software for differential and nonlinear systems
TLDR
PVODE is a portable solver for ordinary differential equation systems, based on robustmathematical algorithms, and targeted at large systems on parallel machines, and is the parallel extension of the earlier sequential solver CVODE.
VFGEN : A Code Generation Tool 1
TLDR
From a single definition of the user's equations, VFGEN can generate code for initial value problem solver libraries, numerical continuation and bifurcation analysis programs, and general purpose computing environments.
A specialized ODE integrator for the efficient computation of parameter sensitivities
TLDR
It is argued that substantially better computational performance can be achieved by exploiting characteristics specific to the problem domain; elements of the methods such as the error estimation could find broader use in other, more general numerical algorithms.
A hybrid, non-split, stiff/RKC, solver for advection–diffusion–reaction equations and its application to low-Mach number combustion
TLDR
A new strategy to couple, in a non-split fashion, stiff integration schemes with explicit, extended-stability predictor-corrector methods with significantly smaller time integration errors is presented.
A Parallel Algorithm To Solve Large Stiff ODE Systems On Grid Systems
TLDR
This paper introduces a parallel algorithm based on the waveform relaxation method coupled with a sequential solver for differential equations systems to solve large stiff ODE systems on distributed clusters, with computing nodes geographically distant from each other.
Optimization of one-parameter family of integration formulae for solving stiff chemical-kinetic ODEs
TLDR
A fast and robust Jacobian-free time-integration method for solving stiff ODEs pertaining to chemical-kinetics is proposed herein and demonstrates higher accuracy compared to the method—Extended Robustness-enhanced numerical algorithm (ERENA)—previously proposed by the authors.
...
...

References

SHOWING 1-9 OF 9 REFERENCES
Reduced storage matrix methods in stiff ODE systems
TLDR
In the context of general nonlinear algebraic systems, this work provides some theoretical foundation for the combined Newton-Krylov method by giving convergence results that include errors due to the difference quotient approximation to the linear operator.
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
We present an iterative method for solving linear systems, which has the property of minimizing at every step the norm of the residual vector over a Krylov subspace. The algorithm is derived from t...
Pragmatic Experiments with Krylov Methods in the Sti ODE Setting
  • Computational Ordinary Di erential Equations,
  • 1992
SIAM J. Sci. Stat. Comput. Reduced Storage Matrix Methods in Stii ODE Systems, J. Appl. Math. & Comp
  • SIAM J. Sci. Stat. Comput. Reduced Storage Matrix Methods in Stii ODE Systems, J. Appl. Math. & Comp
  • 1989
A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
  • SIAM J . Sci . Stat . Comp .
  • 1986
Pragmatic Experiments with Krylov Methods in the Stii ODE Setting, i n Computational Ordinary Diierential Equations
  • J. R. Cash and I. Gladwell Eds
  • 1992
Pragmatic Experiments with Krylov Methods in the Stii ODE Setting, in Computational Ordinary Diierential Equations
  • Pragmatic Experiments with Krylov Methods in the Stii ODE Setting, in Computational Ordinary Diierential Equations
  • 1992
VODE
  • a Variable-Coe cient ODE Solver, SIAM J. Sci. Stat. Comput., 10
  • 1989
SIAM J. Sci. Stat. Comput
  • SIAM J. Sci. Stat. Comput
  • 1989