The interpolation properties of Runge--Kutta methods
Matematičeskoe modelirovanie, Tome 20 (2008) no. 12, pp. 119-128.

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

The Runge–Kutta methods possessing the interpolation properties are examined; all coefficients of these methods belong to the interval $[0,1]$. Explicit and implicit methods up to 5-th order satisfying to the interpolation condition, or almost satisfying to it, are considered.
@article{MM_2008_20_12_a8,
     author = {L. M. Skvortsov},
     title = {The interpolation properties of {Runge--Kutta} methods},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {119--128},
     publisher = {mathdoc},
     volume = {20},
     number = {12},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2008_20_12_a8/}
}
TY  - JOUR
AU  - L. M. Skvortsov
TI  - The interpolation properties of Runge--Kutta methods
JO  - Matematičeskoe modelirovanie
PY  - 2008
SP  - 119
EP  - 128
VL  - 20
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2008_20_12_a8/
LA  - ru
ID  - MM_2008_20_12_a8
ER  - 
%0 Journal Article
%A L. M. Skvortsov
%T The interpolation properties of Runge--Kutta methods
%J Matematičeskoe modelirovanie
%D 2008
%P 119-128
%V 20
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2008_20_12_a8/
%G ru
%F MM_2008_20_12_a8
L. M. Skvortsov. The interpolation properties of Runge--Kutta methods. Matematičeskoe modelirovanie, Tome 20 (2008) no. 12, pp. 119-128. http://geodesic.mathdoc.fr/item/MM_2008_20_12_a8/

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

[2] Dormand J. R., Prince P. J., “A family of embedded Runge-Kutta formulae”, J. Comp. Appl. Math., 6:1 (1980), 19–26 | DOI | MR | Zbl

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

[4] Skvortsov L. M., “Diagonalno neyavnye FSAL-metody Runge–Kutty dlya zhestkikh i differentsialno-algebraicheskikh sistem”, Matem. modelirovanie, 14:2 (2002), 3–17 | MR | Zbl

[5] Skvortsov L. M., “Diagonalno neyavnye metody Runge-Kutty dlya zhestkikh zadach”, Zh. vychisl. matem. i matem. fiz., 46:12 (2006), 2209–2222 | MR

[6] Kalitkin N. N., Panchenko S. L., “Optimalnye skhemy dlya zhestkikh neavtonomnykh sistem”, Matem. modelirovanie, 11:6 (1999), 52–81 | MR

[7] 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

[8] Kozlov O. S., Kondakov D. E., Skvortsov L. M. i dr., Programmnyi kompleks “Modelirovanie v tekhnicheskikh ustroistvakh”, http: model.exponenta.ru/mvtu/20050615.html

[9] Hosea M. E., Shampine L. F., “Analysis and implementation of TR-BDF2”, Appl. Numer. Math., 20:1–2 (1996), 21–37 | DOI | MR | Zbl

[10] Kozlov O. S., Skvortsov L. M., Khodakovskii V. V., Reshenie differentsialnykh i differentsialno-algebraicheskikh uravnenii v programmnom komplekse “MVTU”, http: model.exponenta.ru/mvtu/20051121.html