Geodesic
On one generalization of Runge–Kutta method
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, no. 2 (2006), pp. 167-172 
G. G. Islamov; Y. V. Kogan. On one generalization of Runge–Kutta method. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, no. 2 (2006), pp. 167-172. http://geodesic.mathdoc.fr/item/IIMI_2006_2_a38/
@article{IIMI_2006_2_a38,
     author = {G. G. Islamov and Y. V. Kogan},
     title = {On one generalization of {Runge{\textendash}Kutta} method},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {167--172},
     year = {2006},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2006_2_a38/}
}
TY  - JOUR
AU  - G. G. Islamov
AU  - Y. V. Kogan
TI  - On one generalization of Runge–Kutta method
JO  - Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
PY  - 2006
SP  - 167
EP  - 172
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/IIMI_2006_2_a38/
LA  - ru
ID  - IIMI_2006_2_a38
ER  - 
%0 Journal Article
%A G. G. Islamov
%A Y. V. Kogan
%T On one generalization of Runge–Kutta method
%J Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
%D 2006
%P 167-172
%N 2
%U http://geodesic.mathdoc.fr/item/IIMI_2006_2_a38/
%G ru
%F IIMI_2006_2_a38

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

There are offered to select the coefficients of one Runge–Kutta method generalization with regard to the value of relative error for linearized system of ordinary differential equations. Unlike the known versions of Runge–Kutta methods it is lead to Pade approximation not in zero, but in point nearest the spectrum of multiplied to mesh width the Jacobi matrix in the current mesh point.

[1] Dekker K., Verver Ya., Ustoichivost metodov Runge–Kutty dlya zhestkikh nelineinykh differentsialnykh uravnenii, Mir, M., 1988, 334 pp. | MR

[2] Guld S., Variatsionnye metody v zadachakh o sobstvennykh znacheniyakh. Vvedenie v metod promezhutochnykh zadach Vainshteina, Mir, M., 1970, 328 pp. | MR

[3] Islamov G. G., “Ekstremalnye vozmuscheniya zamknutykh operatorov”, Izv. vuzov. Matematika, 1989, no. 1, 35–41 | MR

[4] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972, 740 pp. | MR | Zbl

[5] Samarskii A. A., Gulin A. V., Chislennye metody, Nauka, M., 1989, 430 pp. | MR

[6] Beiker Dzh. (ml.), Greivs-Morris P., Approksimatsii Pade, Mir, M., 1986, 502 pp. | MR