Computations with inverse Runge–Kutta schemes
Matematičeskoe modelirovanie, Tome 25 (2013) no. 10, pp. 79-96 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

New subclass of fully implicit Runge–Kutta schemes is considered. This subclass has outstanding accuracy and stability characteristics. Implementation details of iterative algorithm for solving stiff systems of ODE and differential-algebraic systems with inverse Runge–Kutta schemes are described.
Keywords: stiff systems, differential-algebraic systems, implicit Runge–Kutta schemes.
@article{MM_2013_25_10_a6,
     author = {N. N. Kalitkin and I. P. Poshivaylo},
     title = {Computations with inverse {Runge{\textendash}Kutta} schemes},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {79--96},
     year = {2013},
     volume = {25},
     number = {10},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2013_25_10_a6/}
}
TY  - JOUR
AU  - N. N. Kalitkin
AU  - I. P. Poshivaylo
TI  - Computations with inverse Runge–Kutta schemes
JO  - Matematičeskoe modelirovanie
PY  - 2013
SP  - 79
EP  - 96
VL  - 25
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/MM_2013_25_10_a6/
LA  - ru
ID  - MM_2013_25_10_a6
ER  - 
%0 Journal Article
%A N. N. Kalitkin
%A I. P. Poshivaylo
%T Computations with inverse Runge–Kutta schemes
%J Matematičeskoe modelirovanie
%D 2013
%P 79-96
%V 25
%N 10
%U http://geodesic.mathdoc.fr/item/MM_2013_25_10_a6/
%G ru
%F MM_2013_25_10_a6
N. N. Kalitkin; I. P. Poshivaylo. Computations with inverse Runge–Kutta schemes. Matematičeskoe modelirovanie, Tome 25 (2013) no. 10, pp. 79-96. http://geodesic.mathdoc.fr/item/MM_2013_25_10_a6/

[1] Khairer E., Nersett S., Vanner G., Reshenie obyknovennykh differentsialnykh uravnenii. Nezhestkie zadachi, Mir, M., 1990, 512 pp. | MR

[2] Khairer E., Vanner G., Reshenie obyknovennykh differentsialnykh uravnenii. Zhestkie i differentsialno-algebraicheskie zadachi, Mir, M., 1999, 685 pp.

[3] Alshina E. A., Zaks E. M., Kalitkin N. N., “Optimalnye parametry yavnykh skhem Runge–Kutty nevysokikh poryadkov”, Matem. modelirovanie, 18:2 (2006), 61–71 | MR | Zbl

[4] Kalitkin N. N., Kuzmina L. V., Integrirovanie zhestkikh sistem differentsialnykh uravnenii, preprint No 80, IPM im. M. V. Keldysha, 1981, 23 pp. | MR

[5] Alshin A. B., Alshina E. A., Limonov A. G., “Dvukhstadiinye kompleksnye skhemy Rozenbroka dlya zhestkikh sistem”, ZhVMiMF, 49:2 (2009), 270–287 | MR

[6] Shirkov P. D., “Optimalno zatukhayuschie skhemy s kompleksnymi koeffitsientami dlya zhestkikh sistem ODU”, Matem. modelirovanie, 4:8 (1992), 47–57 | MR | Zbl

[7] Kalitkin N. N., Poshivailo I. P., “O vychislenii prostykh i kratnykh kornei nelineinogo uravneniya”, Matem. modelirovanie, 20:7 (2008), 57–64 | MR | Zbl

[8] Poshivailo I. P., “Usechennyi mnogomernyi metod Nyutona”, Matem. modelirovanie, 24:1 (2012), 103–108 | MR

[9] Samarskii A. A., Sobol I. M., “Primery chislennogo rascheta temperaturnykh voln”, ZhVMiMF, 3:4 (1963), 702–719 | MR

[10] Kalitkin N. N., Ritus I. V., Kompleksnaya skhema resheniya parabolicheskikh sistem, preprint No 32, IPM im. M. V. Keldysha, 1981, 31 pp. | MR

[11] Rosenbrock H. H., “Some general implicit processes for the numerical solution of differential equations”, Comput. J., 5:4 (1964), 329–330 | DOI | MR