@article{MM_2009_21_12_a5,
author = {A. B. Alshin and E. A. Alshina and A. G. Limonov},
title = {Automatic order conditions symbolic derivation for two-stage complex {Rosenbrock} scheme},
journal = {Matemati\v{c}eskoe modelirovanie},
pages = {76--88},
year = {2009},
volume = {21},
number = {12},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MM_2009_21_12_a5/}
}
TY - JOUR AU - A. B. Alshin AU - E. A. Alshina AU - A. G. Limonov TI - Automatic order conditions symbolic derivation for two-stage complex Rosenbrock scheme JO - Matematičeskoe modelirovanie PY - 2009 SP - 76 EP - 88 VL - 21 IS - 12 UR - http://geodesic.mathdoc.fr/item/MM_2009_21_12_a5/ LA - ru ID - MM_2009_21_12_a5 ER -
A. B. Alshin; E. A. Alshina; A. G. Limonov. Automatic order conditions symbolic derivation for two-stage complex Rosenbrock scheme. Matematičeskoe modelirovanie, Tome 21 (2009) no. 12, pp. 76-88. http://geodesic.mathdoc.fr/item/MM_2009_21_12_a5/
[1] Khairer E., Vanner G., Reshenie obyknovennykh differentsialnykh uravnenii. Zhestkie i differentsialno-algebraicheskie zadachi, Mir, M., 1999, 685 pp.
[2] Kalitkin N. N., “Chislennye metody resheniya zhestkikh sistem”, Matematicheskoe modelirovanie, 7:5 (1995), 8–11 | Zbl
[3] Butcher J. C., Numerical Methods for Ordinary Differential Equations, J. Wiley, Chichester, 2003, 435 pp. | MR | Zbl
[4] Famelis I. Th., Papakostas S. N., Tsitouras Ch., “Symbolic derivation of Runge–Kutta order conditions”, J. Symbol. Comput., 37 (2004), 311–327 | DOI | MR | Zbl
[5] Rosenbrock H. H., “Some general implicit processes for the numerical solution of differential equations”, Comput. J., 5:4 (1963), 329–330 | DOI | MR | Zbl
[6] Alshin A. B., Alshina E. A., Limonov A. G., “Dvukhstadiinye kompleksnye skhemy Rozenbroka dlya zhestkikh sistem”, ZhVMiMF, 49:2 (2009), 270–287 | MR
[7] Shirkov P. D., “Optimalno zatukhayuschie skhemy s kompleksnymi koeffitsientami dlya zhestkikh sistem ODU”, Matematicheskoe modelirovanie, 4:8 (1992), 47–57 | MR
[8] Tygliyan A. V., Filippov S. S., “Elementarnye differentsialy, ikh grafy i kody”, Matematicheskoe modelirovanie, 21:8 (2009), 37–43