Explicit two-step Runge--Kutta methods
Matematičeskoe modelirovanie, Tome 21 (2009) no. 9, pp. 54-65.

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

The explicit two-step Runge–Kutta methods with extended stability regions, and also similar methods with increased stage order are considered. The advantage of two-step methods on a comparison with usual one-step Runge–Kutta methods is shown.
@article{MM_2009_21_9_a5,
     author = {L. M. Skvortsov},
     title = {Explicit two-step {Runge--Kutta} methods},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {54--65},
     publisher = {mathdoc},
     volume = {21},
     number = {9},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2009_21_9_a5/}
}
TY  - JOUR
AU  - L. M. Skvortsov
TI  - Explicit two-step Runge--Kutta methods
JO  - Matematičeskoe modelirovanie
PY  - 2009
SP  - 54
EP  - 65
VL  - 21
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2009_21_9_a5/
LA  - ru
ID  - MM_2009_21_9_a5
ER  - 
%0 Journal Article
%A L. M. Skvortsov
%T Explicit two-step Runge--Kutta methods
%J Matematičeskoe modelirovanie
%D 2009
%P 54-65
%V 21
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2009_21_9_a5/
%G ru
%F MM_2009_21_9_a5
L. M. Skvortsov. Explicit two-step Runge--Kutta methods. Matematičeskoe modelirovanie, Tome 21 (2009) no. 9, pp. 54-65. http://geodesic.mathdoc.fr/item/MM_2009_21_9_a5/

[1] Jackiewich Z., Tracogna S., “A general class of two-step Runge–Kutta methods for ordinary differential equations”, SIAM J. Numer. Anal., 32:5 (1995), 1390–1427 | DOI | MR

[2] Butcher J. C., Tracogna S., “Order conditions for two-step Runge–Kutta methods”, Appl. Numer. Math., 24:2–3 (1997), 351–364 | DOI | MR | Zbl

[3] Hairer E., Wanner G., “Order conditions for general two-step Runge–Kutta methods”, SIAM J. Numer. Anal., 34:6 (1997), 2087–2089 | DOI | MR | Zbl

[4] Bartoszewski Z., Jackiewicz Z., “Construction of two-step Runge–Kutta methods of high order for ordinary differential equations”, Numer. Algorithms, 18:1 (1998), 51–70 | DOI | MR | Zbl

[5] Tracogna S., Welfert B., “Two-step Runge–Kutta: theory and practice”, BIT, 40:4 (2000), 775–799 | DOI | MR | Zbl

[6] Chollom J., Jackiewicz Z., “Construction of two-step Runge–Kutta methods with large regions of absolute stability”, J. Comput. Appl. Math., 157 (2003), 125–137 | DOI | MR | Zbl

[7] Lebedev V. I., “Kak reshat yavnymi metodami zhestkie sistemy differentsialnykh uravnenii”, Vychislitelnye protsessy i sistemy, 8, Nauka, M., 1991, 237–291 | MR

[8] Lebedev V. I., Medovikov A. A., “Yavnyi metod vtorogo poryadka tochnosti dlya resheniya zhestkikh sistem obyknovennykh differentsialnykh uravnenii”, Izv. vuzov. Matematika, 1998, no. 9, 55–63 | MR | Zbl

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

[10] Novikov E. A., Yavnye metody dlya zhestkikh sistem, Nauka, Novosibirsk, 1997, 195 pp. | MR

[11] Skvortsov L. M., “Yavnye adaptivnye metody chislennogo resheniya zhestkikh sistem”, Matem. modelirovanie, 12:12 (2000), 97–107 | MR | Zbl

[12] Skvortsov L. M., “Yavnyi mnogoshagovyi metod chislennogo resheniya zhestkikh differentsialnykh uravnenii”, Zh. vychisl. matem. i matem. fiz., 47:6 (2007), 959–967 | MR

[13] Mazzia F., Magherini C., Iavernaro F., Test set for initial value problem solvers, http://pitagora.dm.uniba.it/~testset

[14] Skvortsov L. M., “Tochnost metodov Runge–Kutty pri reshenii zhestkikh zadach”, Zh. vychisl. matem. i matem. fiz., 43:9 (2003), 1374–1384 | MR | Zbl

[15] Skvortsov L. M., “Yavnye metody Runge–Kutty dlya umerenno zhestkikh zadach”, Zh. vychisl. matem. i matem. fiz., 45:11 (2005), 2017–2030 | MR | Zbl

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

[17] Bogacki P., Shampine L. F., “A 3(2) pair of Runge–Kutta formulas”, Appl. Math. Letters, 2:4 (1989), 321–325 | DOI | MR | Zbl