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RKC

swMATH ID: 808
Software Authors: Sommeijer, B.P.; Shampine, L.F.; Verwer, J.G.
Description: RKC: An explicit solver for parabolic PDEs. An explicit Runge-Kutta-Chebychev algorithm for parabolic partial differential equations is discussed, implemented and tested. This method exploits some remarkable properties of a class of Runge-Kutta formulas of Chebychev type, proposed almost 20 year ago by P. J. van der Houwen and B. P. Sommeijer [Z. Angew. Math. Mech. 60, 479-485 (1980; Zbl 0455.65052)]. An s-stage (s≥2) method is discussed and analytical expressions for its coefficients are derived. An interesting property of this family makes it possible for the algorithm to select at each step the most efficient stable formula and the most efficient time-step. Various computational results and comparisons with other methods are provided.
Homepage: http://www.netlib.org/ode/rkc.f
Keywords: parabolic problems; time integration; stability; numerical examples; grid generation; reaction-diffusion equation; Runge-Kutta-Chebychev algorithm; Runge-Kutta formulas of Chebychev type
Related Software: RODAS; VODE; S-ROCK; IRKC; SERK2; Matlab; PIROCK; SERK2v3; CVODE; MEBDF; M3RK; PETSc; DASSL; MATLAB expm; LSODA; ROWMAP; CHEMKIN; IMPEX; FEniCS; DRFM
Cited in: 138 Documents

Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
RKC: An explicit solver for parabolic PDEs. Zbl 0910.65067
Sommeijer, B. P.; Shampine, L. F.; Verwer, J. G.
1998
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Cited by 239 Authors

8 Verwer, Jan G.
7 Abdulle, Assyr
7 González-Pinto, Severiano
7 Martín-Vaquero, Jesús
7 Najm, Habib N.
7 Sommeijer, Ben P.
6 Pérez Rodríguez, S.
6 Zhang, Yongtao
5 Ray, Jaideep
4 Almuslimani, Ibrahim
4 Hernandez-Abreu, Domingo
4 Kleefeld, B.
4 Seaïd, Mohammed
4 Vilmart, Gilles
4 Weiner, Rüdiger
3 Bermejo, Rodolfo
3 Bochev, M. A.
3 Calhoun, Donna A.
3 Carpio, Jaime
3 El-Amrani, Mofdi
3 Kleefeld, Andreas
3 Kleijn, Chris R.
3 Lefantzi, Sophia
3 Li, Jing-Rebecca
3 Montijano, Juan Ignacio
3 Safta, Cosmin
3 van Veldhuizen, S.
3 Vuik, Cornelis
2 Allan, Benjamin A.
2 Armstrong, Robert C.
2 Aslam, Tariq D.
2 Blaise, Sébastien
2 Cirilli, Stéphane
2 De Souza, Giacomo Rosilho
2 Gear, Charles William
2 Guo, Daniel X.
2 Helzel, Christiane
2 Jiang, Tian
2 Khaliq, Abdul Q. M.
2 Knio, Omar M.
2 Li, Shoufu
2 Marzouk, Youssef M.
2 Medovikov, Alexei A.
2 Meyer, Chad D.
2 Niemeyer, Kyle E.
2 O’Sullivan, Stephen
2 Petzold, Linda Ruth
2 Prieto, Juan Luis
2 Rández, Luis
2 Sandu, Adrian
2 Shampine, Lawrence Fred
2 Sung, Chih-Jen
2 Torrilhon, Manuel
2 Wade, Bruce A.
2 Zhang, Hong
2 Zheng, Zheming
1 Ait-Haddou, Rachid
1 Alavani, Chitra
1 Alber, Mark S.
1 Alberti, Andrea
1 Alzahrani, H. H.
1 Asante-Asamani, E. O.
1 Balsara, Dinshaw S.
1 Beck, Steffen
1 Benson, Steven J.
1 Bergues Cabrales, Luis Enrique
1 Bernholdt, David E.
1 Bhatt, Harish P.
1 Bocher, Philippe
1 Bolaños Vaillant, Sorangel
1 Bruder, Jürgen
1 Brush, Lucien N.
1 Cai, Zhenning
1 Caliari, Marco
1 Calvo, Manuel
1 Castañeda, Antonio Rafael Selva
1 Charron, Martin
1 Chen, Shanqin
1 Cheng, Yuanzhen
1 Croci, Matteo
1 Crouseilles, Nicolas
1 Cruz-Villar, Carlos Alberto
1 Dahlgren, Tamara L.
1 Das, Pratik
1 Dawes, Alan S.
1 de Falco, Carlo
1 Debusschere, Bert J.
1 Deeb, Ahmad Ali
1 del Pozo, Josue Mariño
1 Del Sastre, P. Galán
1 Descombes, Stéphane
1 Diachin, Lori Freitag
1 Doehring, Daniel
1 Dormand, John R.
1 Duarte, Max
1 Dumont, Thierry
1 Eftekhari, Armin
1 Fahrenthold, Eric P.
1 Feodoritova, O. B.
1 Forbes, Lawrence K.
...and 139 more Authors
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Cited in 39 Serials

36 Journal of Computational Physics
15 Journal of Computational and Applied Mathematics
8 Journal of Scientific Computing
8 SIAM Journal on Scientific Computing
7 Applied Mathematics and Computation
7 BIT
7 Applied Numerical Mathematics
4 Mathematics and Computers in Simulation
3 Computational Mathematics and Mathematical Physics
2 Computers & Mathematics with Applications
2 Computer Methods in Applied Mechanics and Engineering
2 Numerische Mathematik
2 Numerical Methods for Partial Differential Equations
2 Combustion Theory and Modelling
1 Computers and Fluids
1 Computer Physics Communications
1 Mathematics of Computation
1 International Journal for Numerical Methods in Engineering
1 SIAM Journal on Numerical Analysis
1 Mathematical and Computer Modelling
1 Applied Mathematical Modelling
1 SIAM Review
1 Communications in Numerical Methods in Engineering
1 Electronic Journal of Differential Equations (EJDE)
1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings
1 Discrete Dynamics in Nature and Society
1 International Journal of Theoretical and Applied Finance
1 The ANZIAM Journal
1 Computational Methods in Applied Mathematics
1 Comptes Rendus. Mathématique. Académie des Sciences, Paris
1 SIAM Journal on Applied Dynamical Systems
1 International Journal of Numerical Analysis and Modeling
1 Progress in Computational Fluid Dynamics
1 Acta Mechanica Sinica
1 Advances in Applied Mathematics and Mechanics
1 Journal of Numerical Mathematics and Stochastics
1 JSIAM Letters
1 Mathematics
1 SIAM/ASA Journal on Uncertainty Quantification

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