LSODE

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 103 articles )

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  1. Hupkes, H.J.; Van Vleck, E.S.: Travelling waves for complete discretizations of reaction diffusion systems (2016)
  2. Peshkov, Ilya; Romenski, Evgeniy: A hyperbolic model for viscous Newtonian flows (2016)
  3. Kroshko, Andrew; Spiteri, Raymond J.: odeToJava: a PSE for the numerical solution of IVPS (2015)
  4. 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)
  5. Pihajoki, Pauli: Explicit methods in extended phase space for inseparable Hamiltonian problems (2015)
  6. Stoyanov, Svetlin: Analytical and numerical investigation on the Duffing oscilator subjected to a polyharmonic force excitation (2015)
  7. Colombo, R.M.; Rossi, E.: On the micro-macro limit in traffic flow (2014)
  8. Rossi, Elena: A justification of a LWR model based on a follow the leader description (2014)
  9. Fischer, Cyril: Massive parallel implementation of ODE solvers. (2013)
  10. 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)
  11. Gautschi, Walter: Numerical analysis. (2012)
  12. Kulikov, G.Yu.: Global error control in adaptive Nordsieck methods (2012)
  13. Miki, K.; Panesi, M.; Prudencio, E.E.; Prudhomme, S.: Probabilistic models and uncertainty quantification for the ionization reaction rate of atomic nitrogen (2012)
  14. Soetaert, Karline; Cash, Jeff; Mazzia, Francesca: Solving differential equations in R. (2012)
  15. 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)
  16. Arul Kumar, M.; Mahesh, Sivasambu; Parameswaran, V.: A `stack’ model of rate-independent polycrystals (2011)
  17. Ibáñez, J.Javier; Hernández, Vicente; Ruiz, Pedro A.; Arias, Enrique: A piecewise-linearized algorithm based on the Krylov subspace for solving stiff ODEs (2011)
  18. Kumbhakarna, Neeraj; Thynell, Stefan T.; Chowdhury, Arindrajit; Lin, Ping: Analysis of RDX-TAGzT pseudo-propellant combustion with detailed chemical kinetics (2011)
  19. Patterson, Robert I.A.; Wagner, Wolfgang; Kraft, Markus: Stochastic weighted particle methods for population balance equations (2011)
  20. Triantafyllou, Savvas P.; Koumousis, Vlasis K.: An inelastic Timoshenko beam element with axial-shear-flexural interaction (2011)

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