ODEPACK, a systematized collection of ODE solvers. ODEPACK is a collection of Fortran solvers for the initial value problem for ordinary differential equation systems. It consists of nine solvers, namely a basic solver called LSODE and eight variants of it -- LSODES, LSODA, LSODAR, LSODPK, LSODKR, LSODI, LSOIBT, and LSODIS. The collection is suitable for both stiff and nonstiff systems. It includes solvers for systems given in explicit form, dy/dt = f(t,y), and also solvers for systems given in linearly implicit form, A(t,y) dy/dt = g(t,y). Two of the solvers use general sparse matrix solvers for the linear systems that arise. Two others use iterative (preconditioned Krylov) methods instead of direct methods for these linear systems. The most recent addition is LSODIS, which solves implicit problems with general sparse treatment of all matrices involved.

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  1. Budanur, Nazmi Burak; Cvitanović, Predrag: Unstable manifolds of relative periodic orbits in the symmetry-reduced state space of the Kuramoto-Sivashinsky system (2017)
  2. Ceccato, Alessandro; Nicolini, Paolo; Frezzato, Diego: Attracting subspaces in a hyper-spherical representation of autonomous dynamical systems (2017)
  3. Tucker, R.W.; Walton, T.J.: On gravitational chirality as the genesis of astrophysical jets (2017)
  4. Gong, Xiaoxue; Xu, Ying; Mahadeo, Vinay; Kaman, Tulin; Larsson, Johan; Glimm, James: Mesh convergence for turbulent combustion (2016)
  5. Ong, Benjamin W.; Haynes, Ronald D.; Ladd, Kyle: Algorithm 965: RIDC methods: a family of parallel time integrators (2016)
  6. Elsheikh, Atiyah: An equation-based algorithmic differentiation technique for differential algebraic equations (2015)
  7. Roa, Javier; Peláez, Jesús: Orbit propagation in Minkowskian geometry (2015)
  8. Chacón, L.; del-Castillo-Negrete, D.; Hauck, C.D.: An asymptotic-preserving semi-Lagrangian algorithm for the time-dependent anisotropic heat transport equation (2014)
  9. Kotov, Dmitry V.; Yee, H.C.; Panesi, Marco; Prabhu, Dinesh K.; Wray, Alan A.: Computational challenges for simulations related to the NASA electric arc shock tube (EAST) experiments (2014)
  10. Novikov, Eugeny A.; Novikov, Anton E.: Variable structure algorithm using explicit and $L$-stable methods (2014)
  11. Schiller, Ulf D.: A unified operator splitting approach for multi-scale fluid-particle coupling in the lattice Boltzmann method (2014)
  12. Fischer, Cyril: Massive parallel implementation of ODE solvers. (2013)
  13. Strohmaier, Alexander; Uski, Ville: An algorithm for the computation of eigenvalues, spectral zeta functions and zeta-determinants on hyperbolic surfaces (2013)
  14. Sulman, Mohamed H.M.; Huntley, Helga S.; Lipphardt, B.L.jun.; Kirwan, A.D.jun.: Leaving flatland: diagnostics for Lagrangian coherent structures in three-dimensional flows (2013)
  15. Alt, Rene; Markov, Svetoslav: Theoretical and computational studies of some bioreactor models (2012)
  16. Hazelton, William D.; Goodman, Gary; Rom, William N.; Tockman, Melvyn; Thornquist, Mark; Moolgavkar, Suresh; Weissfeld, Joel L.; Feng, Ziding: Longitudinal multistage model for lung cancer incidence, mortality, and CT detected indolent and aggressive cancers (2012)
  17. Mazzia, Francesca; Cash, Jeff R.; Soetaert, Karline: A test set for stiff initial value problem solvers in the open source software R: Package \bfdeTestSet (2012)
  18. Monaco, Roberto; Pieraccini, Sandra: A mathematical model for environment evaluations in landscape ecology (2012)
  19. Tamm, Kert; Salupere, Andrus: On the propagation of 1D solitary waves in Mindlin-type microstructured solids (2012)
  20. Abukhdeir, Nasser Mohieddin; Vlachos, Dionisios G.; Katsoulakis, Markos; Plexousakis, Michael: Long-time integration methods for mesoscopic models of pattern-forming systems (2011)

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