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VODE

swMATH ID: 1005
Software Authors: Brown, Peter N.; Byrne, George D.; Hindmarsh, Alan C.
Description: 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.
Homepage: http://www.sciencedirect.com/science/article/pii/S0899824883710153
Keywords: co-polymerization; Ziegler-Natta catalyst; numerical results; performance; VODE; LSODE; DASSL
Related Software: RODAS; CHEMKIN; LSODE; Matlab; DASSL; ODEPACK; MATLAB ODE suite; RKC; DIFSUB; Ode15s; SUNDIALS; ode23s; ode113; ode45; ode23; MEBDF; LSODA; CVODE; GRI-Mech 3.0; RADAU
Cited in: 216 Documents

Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
The taming of a co-polymerization problem with VODE. Zbl 0787.65098
Byrne, George D.
1993
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Cited by 424 Authors

9 Najm, Habib N.
6 Ajaev, Vladimir S.
6 Burrage, Kevin
6 Shampine, Lawrence Fred
5 Bell, John B.
5 Knio, Omar M.
5 Martín-Vaquero, Jesús
5 Woodward, Carol S.
4 Brown, Peter N.
4 Byrne, George D.
4 Calvo, Manuel
4 Day, Marcus S.
4 González-Pinto, Severiano
4 Hindmarsh, Alan C.
4 Podhaisky, Helmut
4 Sandu, Adrian
4 Sommeijer, Ben P.
4 Titi, Edriss Saleh
4 Verwer, Jan G.
3 Bilger, Robert W.
3 Chen, Zheng
3 D’Ambra, Pasqua
3 García-Archilla, Bosco
3 Hernandez-Abreu, Domingo
3 Le Maître, Olivier P.
3 Mazzia, Francesca
3 Montijano, Juan Ignacio
3 Novo, Julia
3 Pérez Rodríguez, S.
3 Petzold, Linda Ruth
3 Rández, Luis
3 Ray, Jaideep
3 Schmitt, Bernhard A.
3 Sherratt, Jonathan A.
3 Singer, Michael A.
3 Soetaert, Karline
3 Vigo-Aguiar, Jesus
3 Weiner, Rüdiger
3 Zhang, Wen
2 Antonelli, Laura
2 Arévalo, Carmen
2 Arias, Enrique
2 Belardini, Paola
2 Cash, Jeff R.
2 Cleary, Matthew John
2 Fabijonas, Bruce R.
2 Fairweather, Michael
2 Ghoniem, Ahmed F.
2 Gladwell, Ian
2 Goussis, Dimitris A.
2 Gregoretti, Francesco
2 Hansen, Michael Alan
2 Hernández, Vicente G.
2 Ibáñez González, Jacinto Javier
2 Jackiewicz, Zdzislaw
2 Jiang, Zonglin
2 Ju, Yiguang
2 Karagozian, Ann R.
2 Kedia, Kushal S.
2 Kelley, Carl T.
2 Kim, Philsu
2 Kim, Sangdong
2 Kleefeld, B.
2 Klentzman, Jill
2 Kosinski, Pawel
2 Lee, Steven L.
2 Lord, Gabriel James
2 Mastorakos, Epaminondas
2 Melander, Mogens V.
2 Miehe, Philipp
2 Moore, Peter K.
2 Oliva, Gennaro
2 Paolucci, Samuel
2 Pham Thi, N. N.
2 Piao, Xiangfan
2 Pohl, Bert
2 Pope, Stephen Bailey
2 Ramos, Higinio
2 Ren, Zhuyin
2 Ruiz, Pedro A.
2 Safta, Cosmin
2 Sidje, Roger B.
2 Stephan, Peter
2 Suhartanto, Heru
2 Sutherland, James Clayton
2 Teng, Honghui
2 Valorani, Mauro
2 Venkatesh, Prasana K.
2 Woolley, R. M.
2 Wyckoff, Peter S.
2 Wynne, Shannon
2 Xie, Qing
2 Yakush, Sergey E.
1 Abdi, Ali
1 Adams, Nikolaus A.
1 Aïd, René
1 Altay, H. Murat
1 Altimari, Pietro
1 Alzahrani, H. H.
1 Angermann, Lutz
...and 324 more Authors
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Cited in 71 Serials

28 Combustion Theory and Modelling
20 Journal of Computational Physics
19 Applied Numerical Mathematics
14 Journal of Computational and Applied Mathematics
10 SIAM Journal on Scientific Computing
8 Computers and Fluids
6 Journal of Fluid Mechanics
5 Computers & Mathematics with Applications
5 ACM Transactions on Mathematical Software
4 Computer Physics Communications
4 Numerical Algorithms
4 Advances in Computational Mathematics
3 Computer Methods in Applied Mechanics and Engineering
3 SIAM Journal on Numerical Analysis
3 International Journal of Computer Mathematics
2 International Journal for Numerical Methods in Fluids
2 Chaos, Solitons and Fractals
2 Shock Waves
2 Journal of Optimization Theory and Applications
2 Journal of Scientific Computing
2 SIAM Journal on Applied Mathematics
2 Computational Statistics and Data Analysis
2 Physics of Fluids
2 ETNA. Electronic Transactions on Numerical Analysis
2 Journal of Mathematical Chemistry
2 Computing and Visualization in Science
2 Flow, Turbulence and Combustion
2 JNAIAM. Journal of Numerical Analysis, Industrial and Applied Mathematics
1 Astronomy and Astrophysics
1 Astrophysics and Space Science
1 Fluid Dynamics
1 IMA Journal of Numerical Analysis
1 International Journal of Heat and Mass Transfer
1 International Journal of Multiphase Flow
1 Journal of Engineering Mathematics
1 Nonlinearity
1 Theoretical and Computational Fluid Dynamics
1 Applied Mathematics and Computation
1 BIT
1 International Journal for Numerical Methods in Engineering
1 Kyungpook Mathematical Journal
1 Mathematics and Computers in Simulation
1 Numerische Mathematik
1 Theoretical Population Biology
1 SIAM Journal on Scientific and Statistical Computing
1 Physica D
1 Mathematical and Computer Modelling
1 IMPACT of Computing in Science and Engineering
1 Journal of Dynamics and Differential Equations
1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
1 Mathematical Problems in Engineering
1 Nonlinear Dynamics
1 Chaos
1 Mathematical and Computer Modelling of Dynamical Systems
1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
1 Communications in Nonlinear Science and Numerical Simulation
1 Journal of Turbulence
1 Matematicheskoe Modelirovanie
1 SIAM Journal on Applied Dynamical Systems
1 Journal of Cosmology and Astroparticle Physics
1 Texts in Applied Mathematics
1 Acta Mechanica Sinica
1 Communications in Computational Physics
1 Mathematical Modelling of Natural Phenomena
1 Algorithms
1 Advances in Applied Mathematics and Mechanics
1 Communications in Mathematical Research
1 Statistics and Computing
1 Numerical Algebra, Control and Optimization
1 Journal of Theoretical Biology
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