Geodesic
Automatic order conditions symbolic derivation for two-stage complex Rosenbrock scheme
Matematičeskoe modelirovanie, Tome 21 (2009) no. 12, pp. 76-88 
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/
@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  - 
%0 Journal Article
%A A. B. Alshin
%A E. A. Alshina
%A A. G. Limonov
%T Automatic order conditions symbolic derivation for two-stage complex Rosenbrock scheme
%J Matematičeskoe modelirovanie
%D 2009
%P 76-88
%V 21
%N 12
%U http://geodesic.mathdoc.fr/item/MM_2009_21_12_a5/
%G ru
%F MM_2009_21_12_a5

Voir la notice de l'article provenant de la source Math-Net.Ru

It is well known, that Rosenbrock's type schemes have good performance for stiff systems. In this paper the new algorithm for automatic order conditions symbolic derivation for Rosenbrock’s type scheme with complex coefficients is introduced. Also programming issues explained in details.

[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