LSODE (Livermore Solver for Ordinary Differential Equations) solves stiff and nonstiff systems of the form dy/dt = f(t,y). In the stiff case, it treats the Jacobian matrix df/dy as either a dense (full) or a banded matrix, and as either user-supplied or internally approximated by difference quotients. It uses Adams methods (predictor-corrector) in the nonstiff case, and Backward Differentiation Formula (BDF) methods (the Gear methods) in the stiff case. The linear systems that arise are solved by direct methods (LU factor/solve). LSODE supersedes the older GEAR and GEARB packages, and reflects a complete redesign of the user interface and internal organization, with some algorithmic improvements. LSODE is available in separate double and single precision versions, called DLSODE and SLSODE. Documentation on the usage of DLSODE/SLSODE is provided in the initial block of comment lines in the source file, which includes a simple example. A demonstration program (in seperate double/single precision versions) is also available.

References in zbMATH (referenced in 108 articles )

Showing results 1 to 20 of 108.
Sorted by year (citations)

1 2 3 4 5 6 next

  1. Capistrán, Marcos A.; Christen, J.Andrés; Donnet, Sophie: Bayesian analysis of ODEs: solver optimal accuracy and Bayes factors (2016)
  2. Hupkes, H.J.; Van Vleck, E.S.: Travelling waves for complete discretizations of reaction diffusion systems (2016)
  3. Peshkov, Ilya; Romenski, Evgeniy: A hyperbolic model for viscous Newtonian flows (2016)
  4. Kroshko, Andrew; Spiteri, Raymond J.: odeToJava: a PSE for the numerical solution of IVPS (2015)
  5. Mangold, Michael; Feng, Lihong; Khlopov, Dmytro; Palis, Stefan; Benner, Peter; Binev, Daniel; Seidel-Morgenstern, Andreas: Nonlinear model reduction of a continuous fluidized bed crystallizer (2015)
  6. Miki, Kenji; Panesi, Marco; Prudhomme, Serge: Systematic validation of non-equilibrium thermochemical models using Bayesian inference (2015)
  7. Pihajoki, Pauli: Explicit methods in extended phase space for inseparable Hamiltonian problems (2015)
  8. Stoyanov, Svetlin: Analytical and numerical investigation on the Duffing oscilator subjected to a polyharmonic force excitation (2015)
  9. Tang, Yu-Hang; Kudo, Shuhei; Bian, Xin; Li, Zhen; Karniadakis, George Em: Multiscale universal interface: a concurrent framework for coupling heterogeneous solvers (2015)
  10. Colombo, R.M.; Rossi, E.: On the micro-macro limit in traffic flow (2014)
  11. Rossi, Elena: A justification of a LWR model based on a follow the leader description (2014)
  12. Fischer, Cyril: Massive parallel implementation of ODE solvers. (2013)
  13. Kwakkel, Marcel; Breugem, Wim-Paul; Boersma, Bendiks Jan: Extension of a CLSVOF method for droplet-laden flows with a coalescence/breakup model (2013)
  14. Charest, Marc R.J.; Groth, Clinton P.T.; Gülder, Ömer L.: Solution of the equation of radiative transfer using a Newton-Krylov approach and adaptive mesh refinement (2012)
  15. Gautschi, Walter: Numerical analysis. (2012)
  16. Kulikov, G.Yu.: Global error control in adaptive Nordsieck methods (2012)
  17. Miki, K.; Panesi, M.; Prudencio, E.E.; Prudhomme, S.: Probabilistic models and uncertainty quantification for the ionization reaction rate of atomic nitrogen (2012)
  18. Soetaert, Karline; Cash, Jeff; Mazzia, Francesca: Solving differential equations in R. (2012)
  19. Zhang, Xudong; Fan, Baochun; Gui, Mingyue; Pan, Zhenhua; Dong, Gang: Numerical study on three-dimensional flow field of continuously rotating detonation in a toroidal chamber (2012)
  20. Arul Kumar, M.; Mahesh, Sivasambu; Parameswaran, V.: A `stack’ model of rate-independent polycrystals (2011)

1 2 3 4 5 6 next