One-stage Rosenbrock method with complex coefficients and automatic time step evaluation
Matematičeskoe modelirovanie, Tome 23 (2011) no. 3, pp. 127-138.

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

Well-known one-stage Rosenbrock scheme with complex coefficients is generalized to the case which allows to make a simple estimation of the truncation error. New version of such a scheme preserves all properties of the old one (such as $A$-stability and $L$-decrementation) and makes possible to choose step of integration automatically with the use of correction procedure. Testing of strategy of time step evaluation as well as of new method has been done with the use of well known and original nonlinear differential equations and systems of equations include nonlinear equation of the heat conduction.
Keywords: Rosenbrock methods, stiff problems, method of lines, automatic time step evaluation.
Mots-clés : monotonous schemes
@article{MM_2011_23_3_a10,
     author = {A. M. Zubanov and N. I. Kokonkov and P. D. Shirkov},
     title = {One-stage {Rosenbrock} method with complex coefficients and automatic time step evaluation},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {127--138},
     publisher = {mathdoc},
     volume = {23},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2011_23_3_a10/}
}
TY  - JOUR
AU  - A. M. Zubanov
AU  - N. I. Kokonkov
AU  - P. D. Shirkov
TI  - One-stage Rosenbrock method with complex coefficients and automatic time step evaluation
JO  - Matematičeskoe modelirovanie
PY  - 2011
SP  - 127
EP  - 138
VL  - 23
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2011_23_3_a10/
LA  - ru
ID  - MM_2011_23_3_a10
ER  - 
%0 Journal Article
%A A. M. Zubanov
%A N. I. Kokonkov
%A P. D. Shirkov
%T One-stage Rosenbrock method with complex coefficients and automatic time step evaluation
%J Matematičeskoe modelirovanie
%D 2011
%P 127-138
%V 23
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2011_23_3_a10/
%G ru
%F MM_2011_23_3_a10
A. M. Zubanov; N. I. Kokonkov; P. D. Shirkov. One-stage Rosenbrock method with complex coefficients and automatic time step evaluation. Matematičeskoe modelirovanie, Tome 23 (2011) no. 3, pp. 127-138. http://geodesic.mathdoc.fr/item/MM_2011_23_3_a10/

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

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

[3] Rosenbrock H., “Some general implicit processes for numerical solution of differential equations”, Computer J., 5:4 (1963), 329–330 | DOI | MR | Zbl

[4] Kalitkin N. N., Kuzmina L. V., Integrirovanie zhestkikh sistem differentsialnykh uravnenii, Preprint No 80, IPM im. M. V. Keldysha AN SSSR, 1981

[5] Shirkov P. D., “Raznostnye skhemy dlya chislennogo integrirovaniya neavtonomnykh zhestkikh ODU”, Zh. vychisl. matem. i matem. fiz., 27:1 (1987), 131–135 | MR | Zbl

[6] Dnestrovskaya E. Yu., Kalitkin N. N., Ritus I. V., “Reshenie uravnenii v chastnykh proizvodnykh skhemami s kompleksnymi koeffitsientami”, Matem. modelirov., 3:9 (1991), 114–127 | MR | Zbl

[7] Guzhev D. S., Kalitkin N. N., “Uravnenie Byurgersa – test dlya chislennykh metodov”, Matem. modelirovanie, 7:10 (1995), 12–32 | MR | Zbl

[8] Anistratov D. Yu., Goldin V. Ya., “Reaktor na bystrykh neitronakh v samoreguliruemom neitronno-yadernom rezhime”, Matem. modelirovanie, 7:4 (1995), 99–127 | MR | Zbl

[9] Guzhev D. S., Zaifert P., Kalitkin N. N., Shirkov P. D., “Chislennye metody dlya zadach khimicheskoi kinetiki s diffuziei”, Matematich. modelirovanie, 4:1 (1992), 98–110

[10] Alexander R., “Diagonally implicit Runge–Kutta methods for stiff ODEs”, SIAM J. N. A., 14:6 (1977), 1006–1021 | DOI | MR | Zbl

[11] Kochetkov K. A., Shirkov P. D., “$L$-zatukhayuschie ROW-metody s tochnoi otsenkoi lokalnoi pogreshnosti”, Matematicheskoe modelirovanie, 13:8 (2001), 35–43 | Zbl

[12] Kochetkov K. A., Shirkov P. D., “$L$-zatukhayuschie ROW metody tretego poryadka tochnosti”, Zh. vych. matemat. i matem. fiz., 37:6 (1997), 699–710 | MR | Zbl

[13] Butcher J., The numerical analysis of ordinary differential equations, Runge–Kutta and general linear methods, John Wiley Sons Ltd., London, 1987 | MR | Zbl