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 123 articles )

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  1. Ozenda, Olivier; Saramito, Pierre; Chambon, Guillaume: Tensorial rheological model for concentrated non-colloidal suspensions: normal stress differences (2020)
  2. Aggarwal, Manu; Cogan, Nicholas; Bertram, Richard: Where to look and how to look: combining global sensitivity analysis with fast/slow analysis to study multi-timescale oscillations (2019)
  3. Montijano, J. I.; Podhaisky, H.; Rández, L.; Calvo, M.: A family of (L)-stable singly implicit peer methods for solving stiff IVPs (2019)
  4. Aggarwal, Manu; Hussaini, M. Y.; De La Fuente, Leonardo; Navarrete, Fernando; Cogan, N. G.: A framework for model analysis across multiple experiment regimes: investigating effects of zinc on \textitXylellafastidiosa as a case study (2018)
  5. Asgharzadeh, Hafez; Borazjani, Iman: A Newton-Krylov method with an approximate analytical Jacobian for implicit solution of Navier-Stokes equations on staggered overset-curvilinear grids with immersed boundaries (2017)
  6. Essa, Saad; Argeso, Hakan: Elastic analysis of variable profile and polar orthotropic FGM rotating disks for a variation function with three parameters (2017)
  7. Feng, Fan; Chi, Xuebin; Wang, Zifa; Li, Jie; Jiang, Jinrong; Yang, Wenyi: A nonnegativity preserved efficient chemical solver applied to the air pollution forecast (2017)
  8. Yau, Chun Yip; Hui, Tsz Shing: LARS-type algorithm for group Lasso (2017)
  9. Capistrán, Marcos A.; Christen, J. Andrés; Donnet, Sophie: Bayesian analysis of ODEs: solver optimal accuracy and Bayes factors (2016)
  10. Hupkes, H. J.; Van Vleck, E. S.: Travelling waves for complete discretizations of reaction diffusion systems (2016)
  11. Larbat, Romain; Robin, Christophe; Lillo, Cathrine; Drengstig, Tormod; Ruoff, Peter: Modeling the diversion of primary carbon flux into secondary metabolism under variable nitrate and light/dark conditions (2016)
  12. Peshkov, Ilya; Romenski, Evgeniy: A hyperbolic model for viscous Newtonian flows (2016)
  13. Kroshko, Andrew; Spiteri, Raymond J.: odeToJava: a PSE for the numerical solution of IVPS (2015)
  14. 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)
  15. Miki, Kenji; Panesi, Marco; Prudhomme, Serge: Systematic validation of non-equilibrium thermochemical models using Bayesian inference (2015)
  16. Pihajoki, Pauli: Explicit methods in extended phase space for inseparable Hamiltonian problems (2015)
  17. Stoyanov, Svetlin: Analytical and numerical investigation on the Duffing oscilator subjected to a polyharmonic force excitation (2015)
  18. Tang, Yu-Hang; Kudo, Shuhei; Bian, Xin; Li, Zhen; Karniadakis, George Em: Multiscale universal interface: a concurrent framework for coupling heterogeneous solvers (2015)
  19. Batra, R. C.; Xiao, J.: Analysis of adiabatic shear bands in thermo-elasto-viscoplastic materials by using piece-wise discontinuous basis functions (2014)
  20. Colombo, R. M.; Rossi, E.: On the micro-macro limit in traffic flow (2014)

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