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. Elsheikh, Atiyah: An equation-based algorithmic differentiation technique for differential algebraic equations (2015)
  2. Roa, Javier; Peláez, Jesús: Orbit propagation in Minkowskian geometry (2015)
  3. Novikov, Eugeny A.; Novikov, Anton E.: Variable structure algorithm using explicit and $L$-stable methods (2014)
  4. Fischer, Cyril: Massive parallel implementation of ODE solvers. (2013)
  5. Strohmaier, Alexander; Uski, Ville: An algorithm for the computation of eigenvalues, spectral zeta functions and zeta-determinants on hyperbolic surfaces (2013)
  6. 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)
  7. Alt, Rene; Markov, Svetoslav: Theoretical and computational studies of some bioreactor models (2012)
  8. 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)
  9. 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)
  10. Monaco, Roberto; Pieraccini, Sandra: A mathematical model for environment evaluations in landscape ecology (2012)
  11. Tamm, Kert; Salupere, Andrus: On the propagation of 1D solitary waves in Mindlin-type microstructured solids (2012)
  12. Abukhdeir, Nasser Mohieddin; Vlachos, Dionisios G.; Katsoulakis, Markos; Plexousakis, Michael: Long-time integration methods for mesoscopic models of pattern-forming systems (2011)
  13. Kim, Sangdong; Kwon, Jongkyum; Piao, Xiangfan; Kim, Philsu: A Chebyshev collocation method for stiff initial value problems and its stability (2011)
  14. Masarati, Pierangelo: Adding kinematic constraints to purely differential dynamics (2011)
  15. Placzek, A.; Tran, D.-M.; Ohayon, R.: A nonlinear POD-Galerkin reduced-order model for compressible flows taking into account rigid body motions (2011)
  16. Sherratt, Jonathan A.: Pattern solutions of the Klausmeier model for banded vegetation in semi-arid environments. II: Patterns with the largest possible propagation speeds (2011)
  17. Van Beek, Johannes H.G.M.; Supandi, Farahaniza; Gavai, Anand K.; De Graaf, Albert A.; Binsl, Thomas W.; Hettling, Hannes: Simulating the physiology of athletes during endurance sports events: modelling human energy conversion and metabolism (2011)
  18. Yuan, Qiang; Liang, Dong: A new multiple sub-domain RS-HDMR method and its application to tropospheric alkane photochemistry model (2011)
  19. Begon, Mickaël; Colloud, Floren; Sardain, Philippe: Lower limb contribution in kayak performance: Modelling, simulation and analysis (2010)
  20. Betts, John T.: Practical methods for optimal control and estimation using nonlinear programming (2010)

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