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.
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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
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20 Journal of Computational Physics
19 Applied Numerical Mathematics
14 Journal of Computational and Applied Mathematics
10 SIAM Journal on Scientific Computing
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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
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2 Flow, Turbulence and Combustion
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