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. Allen, Henry R.; Ptashnyk, Mariya: Mathematical modelling of auxin transport in plant tissues: flux meets signalling and growth (2020)
  2. Kondo, Shintaro; Numata, Ryusuke: Existence theorem and global asymptotical stability for low-dimensional dynamical models of plasma turbulence (2020)
  3. Moradi, A.; Sharifi, M.; Abdi, A.: Transformed implicit-explicit second derivative diagonally implicit multistage integration methods with strong stability preserving explicit part (2020)
  4. Yalnız, Gökhan; Budanur, Nazmi Burak: Inferring symbolic dynamics of chaotic flows from persistence (2020)
  5. Duintjer Tebbens, Jurjen; Matonoha, Ctirad; Matthios, Andreas; Papáček, Štěpán: On parameter estimation in an in vitro compartmental model for drug-induced enzyme production in pharmacotherapy. (2019)
  6. Izzo, G.; Jackiewicz, Z.: Transformed implicit-explicit DIMSIMs with strong stability preserving explicit part (2019)
  7. Peets, Tanel; Tamm, Kert: Mathematics of nerve signals (2019)
  8. Salupere, Andrus; Lints, Martin; Ilison, Lauri: Emergence of solitonic structures in hierarchical Korteweg-de Vries systems (2019)
  9. Ansmann, Gerrit: Efficiently and easily integrating differential equations with JiTCODE, JiTCDDE, and JiTCSDE (2018)
  10. Golubyatnikov, V. P.; Kazantsev, M. V.; Kirillova, N. E.; Bukharina, T. A.; Furman, D. P.: Mathematical and numerical models of two asymmetric gene networks (2018)
  11. Kacewicz, Bolesław: Adaptive mesh point selection for the efficient solution of scalar IVPs (2018)
  12. Leite, M. C. A.; Chen-Charpentier, B.; Agusto, F. B.: A mathematical model of tree harvesting in age-structured forests subject to beetle infestations (2018)
  13. Morales, J. E.; James, G.; Tonnelier, Arnaud: Solitary waves in the excitable Burridge-Knopoff model (2018)
  14. Reinharz, Vladimir; Dahari, Harel; Barash, Danny: Numerical schemes for solving and optimizing multiscale models with age of hepatitis C virus dynamics (2018)
  15. Budanur, Nazmi Burak; Cvitanović, Predrag: Unstable manifolds of relative periodic orbits in the symmetry-reduced state space of the Kuramoto-Sivashinsky system (2017)
  16. Buffo, A.; Vanni, M.; Marchisio, Daniele L.: Simulation of a reacting gas-liquid bubbly flow with CFD and PBM: validation with experiments (2017)
  17. Ceccato, Alessandro; Nicolini, Paolo; Frezzato, Diego: Attracting subspaces in a hyper-spherical representation of autonomous dynamical systems (2017)
  18. Essa, Saad; Argeso, Hakan: Elastic analysis of variable profile and polar orthotropic FGM rotating disks for a variation function with three parameters (2017)
  19. Szatmary, Alex C.; Nossal, R.: Determining whether observed eukaryotic cell migration indicates chemotactic responsiveness or random chemokinetic motion (2017)
  20. Tamm, Kert; Peets, Tanel; Engelbrecht, Jüri; Kartofelev, Dmitri: Negative group velocity in solids (2017)

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