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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  1. González-Pinto, S.; Hernández-Abreu, D.: Splitting-methods based on approximate matrix factorization and Radau-IIA formulas for the time integration of advection diffusion reaction PDEs (2016)
  2. Hansen, M.A.; Sutherland, J.C.: Pseudotransient continuation for combustion simulation with detailed reaction mechanisms (2016)
  3. Hupkes, H.J.; Van Vleck, E.S.: Travelling waves for complete discretizations of reaction diffusion systems (2016)
  4. Kleefeld, B.; Martín-Vaquero, J.: SERK2v3: Solving mildly stiff nonlinear partial differential equations (2016)
  5. Kublik, Richard A.; Chopp, David L.: A locally adaptive time stepping algorithm for the solution to reaction diffusion equations on branched structures (2016)
  6. Morii, Youhi; Terashima, Hiroshi; Koshi, Mitsuo; Shimizu, Taro; Shima, Eiji: ERENA: a fast and robust Jacobian-free integration method for ordinary differential equations of chemical kinetics (2016)
  7. Motheau, E.; Abraham, J.: A high-order numerical algorithm for DNS of low-Mach-number reactive flows with detailed chemistry and quasi-spectral accuracy (2016)
  8. Zhang, Weiqun; Almgren, Ann; Day, Marcus; Nguyen, Tan; Shalf, John; Unat, Didem: BoxLib with tiling: an adaptive mesh refinement software framework (2016)
  9. Gonzalez-Pinto, S.; Hernandez-Abreu, D.; Perez-Rodriguez, S.: AMF-Runge-Kutta formulas and error estimates for the time integration of advection diffusion reaction PDEs (2015)
  10. Khenner, M.; Bandegi, M.: Electromigration-driven evolution of the surface morphology and composition for a bi-component solid film (2015)
  11. Kroshko, Andrew; Spiteri, Raymond J.: odeToJava: a PSE for the numerical solution of IVPS (2015)
  12. Savard, B.; Xuan, Y.; Bobbitt, B.; Blanquart, G.: A computationally-efficient, semi-implicit, iterative method for the time-integration of reacting flows with stiff chemistry (2015)
  13. González-Pinto, S.; Hernández-Abreu, D.; Pérez-Rodríguez, S.: Rosenbrock-type methods with inexact AMF for the time integration of advection-diffusion-reaction PDEs (2014)
  14. Hipp, David; Hochbruck, Marlis; Ostermann, Alexander: An exponential integrator for non-autonomous parabolic problems (2014)
  15. Kedia, Kushal S.; Safta, Cosmin; Ray, Jaideep; Najm, Habib N.; Ghoniem, Ahmed F.: A second-order coupled immersed boundary-SAMR construction for chemically reacting flow over a heat-conducting Cartesian grid-conforming solid (2014)
  16. Paolucci, Samuel; Zikoski, Zachary J.; Grenga, Temistocle: WAMR: an adaptive wavelet method for the simulation of compressible reacting flow. Part II: The parallel algorithm (2014)
  17. Capecelatro, Jesse; Desjardins, Olivier: An Euler-Lagrange strategy for simulating particle-laden flows (2013)
  18. Thomas, Vaughan L.: Effect of particle size distribution on particle based composite anode models (2013)
  19. Ajaev, Vladimir S.: Interfacial fluid mechanics. A mathematical modeling approach. (2012)
  20. Freytag, B.; Steffen, M.; Ludwig, H.-G.; Wedemeyer-Böhm, S.; Schaffenberger, W.; Steiner, O.: Simulations of stellar convection with CO5BOLD (2012)

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