VODE: A variable-coefficient ODE solver. This paper is concerned with the development of a new software package VODE for the numerical solution of (stiff and non-stiff) systems of ordinary differential equations. The new package can be considered as an up to day version of the well known EPISODE by the second and the third author [ACM Trans. Math. Software 1, 71-96 (1975; Zbl 0311.65049)]. Among the improvements that have been introduced we may mention a flexible user interface which is very similar to that of the ODEPACK solver LSODE. Also new algorithms for initial stepsize and stepsize and order change are used. Moreover, in the stiff case, the code has the possibility to save the Jacobian matrix to be used in the solution of the implicit equations by quasi Newton methods. In this paper the authors consider also the fixed leading instead of the full variable coefficient version of the backward differentiation formula methods for stiff systems. They find that the first ones performs better on some problems, but the authors say that further testing is needed to have a clear understanding of their performance. The paper ends with some comparison tests with EPISODE using one and two-dimensional versions of a diurnal kinetics-transport problem. The dimensions are between 50 and 400 and the Jacobian is banded in all cases. It is found that the run time is reduced by an amount between 40 and 60 percent.

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  2. Borisov, V. E.; Yakush, S. E.; Sysoeva, E. Ya.: Numerical simulation of cellular flame propagation in narrow gaps (2022)
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  10. Tang, Xiao; Xiao, Aiguo: Improved Runge-Kutta-Chebyshev methods (2020)
  11. Xie, Wenwen; Xie, Qing; Zhou, Hua; Ren, Zhuyin: An exponential distribution scheme for the two-way coupling in transported PDF method for dilute spray combustion (2020)
  12. You, Jiaping; Yang, Yue: Modelling of the turbulent burning velocity based on Lagrangian statistics of propagating surfaces (2020)
  13. Ceccato, Alessandro; Nicolini, Paolo; Frezzato, Diego: Recasting the mass-action rate equations of open chemical reaction networks into a universal quadratic format80A30 (2019)
  14. Dong, Haibo; Fu, Lin; Zhang, Fan; Liu, Yu; Liu, Jun: Detonation simulations with a fifth-order TENO scheme (2019)
  15. Kabanov, Dmitry I.; Kasimov, Aslan R.: A minimal hyperbolic system for unstable shock waves (2019)
  16. Lucchesi, M.; Alzahrani, H. H.; Safta, C.; Knio, O. M.: A hybrid, non-split, stiff/RKC, solver for advection-diffusion-reaction equations and its application to low-Mach number combustion (2019)
  17. Monegaglia, F.; Tubino, M.; Zolezzi, G.: Interaction between curvature-driven width oscillations and channel curvature in evolving meander bends (2019)
  18. Overstall, Antony M.; Woods, David C.; Martin, Kieran J.: Bayesian prediction for physical models with application to the optimization of the synthesis of pharmaceutical products using chemical kinetics (2019)
  19. Schober, Michael; Särkkä, Simo; Hennig, Philipp: A probabilistic model for the numerical solution of initial value problems (2019)
  20. Wang, Jian-Hang; Pan, Shucheng; Hu, Xiangyu Y.; Adams, Nikolaus A.: Partial characteristic decomposition for multi-species Euler equations (2019)

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