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 135 articles )

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  1. Solomatin, Roman S.; Semenov, Ilya V.: Modelling of hydrogen-air supersonic mixing and combustion in near-wall region (2021)
  2. Su, Wei-Hung; Chou, Ching-Shan; Xiu, Dongbin: Deep learning of biological models from data: applications to ODE models (2021)
  3. Tokar, V. I.: Self-consistent renormalization group approach to continuous phase transitions in alloys: application to ordering in (\beta)-brass (2021)
  4. Arévalo, Carmen; Jonsson-Glans, Erik; Olander, Josefine; Selva Soto, Monica; Söderlind, Gustaf: A software platform for adaptive high order multistep methods (2020)
  5. Hao, Yuxin; Gu, Xiaojun; Zhang, Wei; Chen, Jie: Transient response of high dimensional nonlinear dynamic system for a rotating cantilever twisted plate (2020)
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  7. Ozenda, Olivier; Saramito, Pierre; Chambon, Guillaume: Tensorial rheological model for concentrated non-colloidal suspensions: normal stress differences (2020)
  8. Wei, Tao; Zhang, Mengqi: Rayleigh-Taylor unstable condensing liquid layers with nonlinear effects of interfacial convection and diffusion of vapour (2020)
  9. 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)
  10. Amato, Davide; Bombardelli, Claudio; Baù, Giulio; Morand, Vincent; Rosengren, Aaron J.: Non-averaged regularized formulations as an alternative to semi-analytical orbit propagation methods (2019)
  11. Barton, Philip T.: An interface-capturing Godunov method for the simulation of compressible solid-fluid problems (2019)
  12. Montijano, J. I.; Podhaisky, H.; Rández, L.; Calvo, M.: A family of (L)-stable singly implicit peer methods for solving stiff IVPs (2019)
  13. 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)
  14. 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)
  15. Bartuccelli, Michele; Deane, Jonathan; Gentile, Guido: Fast numerics for the spin orbit equation with realistic tidal dissipation and constant eccentricity (2017)
  16. Essa, Saad; Argeso, Hakan: Elastic analysis of variable profile and polar orthotropic FGM rotating disks for a variation function with three parameters (2017)
  17. 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)
  18. Galuzio, Paulo P.; Benkadda, S.; Lopes, S. R.: Characterization of intermittency at the onset of turbulence in the forced and damped nonlinear Schrödinger equation (2017)
  19. Yau, Chun Yip; Hui, Tsz Shing: LARS-type algorithm for group Lasso (2017)
  20. Capistrán, Marcos A.; Christen, J. Andrés; Donnet, Sophie: Bayesian analysis of ODEs: solver optimal accuracy and Bayes factors (2016)

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