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.

References in zbMATH (referenced in 152 articles )

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  1. Hill, D. J.; Pullin, D.; Ortiz, M.; Meiron, D.: An Eulerian hybrid WENO centered-difference solver for elastic-plastic solids (2010)
  2. Karline Soetaert; Thomas Petzoldt: Inverse Modelling, Sensitivity and Monte Carlo Analysis in R Using Package FME (2010) not zbMATH
  3. Karline Soetaert; Thomas Petzoldt; R. Setzer: Solving Differential Equations in R: Package deSolve (2010) not zbMATH
  4. López, David J.; Romay, José G.: Implementing Adams methods with preassigned stepsize ratios (2010)
  5. Sánchez, J.; Net, M.; Simó, C.: Computation of invariant tori by Newton-Krylov methods in large-scale dissipative systems (2010)
  6. Aleman-Meza, Boanerges; Yu, Yihai; Schüttler, Heinz-Bernd; Arnold, Jonathan; Taha, Thiab R.: KINSOLVER: A simulator for computing large ensembles of biochemical and gene regulatory networks (2009)
  7. Foster, John T. jun.; Barhorst, Alan A.; Wong, C. N. (Simon); Bement, Matthew T.: Modeling loose joints in elastic structures- experimental results and validation (2009)
  8. Ilison, Lauri; Salupere, Andrus: Propagation of (sech^2)-type solitary waves in hierarchical KdV-type systems (2009)
  9. King, J. R.; Münch, A.; Wagner, B. A.: Linear stability analysis of a sharp-interface model for dewetting thin films (2009)
  10. Momen, G.; Hermosilla, G.; Michau, A.; Pons, M.; Firdaous, M.; Marty, Ph.; Hassouni, K.: Experimental and numerical investigation of the thermal effects during hydrogen charging in packed bed storage tank (2009)
  11. Piggott, M. D.; Farrell, P. E.; Wilson, C. R.; Gorman, G. J.; Pain, C. C.: Anisotropic mesh adaptivity for multi-scale ocean modelling (2009)
  12. Calvo, M.; González-Pinto, S.; Montijano, J. I.: Global error estimation based on the tolerance proportionality for some adaptive Runge-Kutta codes (2008)
  13. Fox, R. O.; Laurent, F.; Massot, M.: Numerical simulation of spray coalescence in an Eulerian framework: direct quadrature method of moments and multi-fluid method (2008)
  14. Gamito, Manuel N.; Maddock, Steve C.: Topological correction of hypertextured implicit surfaces for ray casting (2008) ioport
  15. Hernández, Vicente; Ibáñez, Jacinto Javier; Peinado, Jesús; Arias, Enrique: A GMRES-based BDF method for solving differential Riccati equations (2008)
  16. Okazaki, Noriaki; Asano, Ryoji; Kinoshita, Takashi; Chuman, Hiroshi: Simple computational models of type I/type II cells in Fas signaling-induced apoptosis (2008)
  17. Salupere, A.; Tamm, K.; Engelbrecht, J.: Numerical simulation of interaction of solitary deformation waves in microstructured solids (2008)
  18. Adams, B. M.; Banks, H. T.; Davidian, M.; Rosenberg, E. S.: Estimation and prediction with HIV-treatment interruption data (2007)
  19. Arias, Enrique; Hernández, Vicente; Ibáñez, Jacinto Javier; Peinado, Jesús: A fixed point-based BDF method for solving differential Riccati equations (2007)
  20. Descombes, Stéphane; Dumont, Thierry; Louvet, Violaine; Massot, Marc: On the local and global errors of splitting approximations of reaction-diffusion equations with high spatial gradients (2007)