Geodesic
A simple technique for constructing two-step Runge–Kutta methods
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 11, pp. 1920-1930 Cet article a éte moissonné depuis la source Math-Net.Ru

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A technique is proposed for constructing two-step Runge–Kutta methods on the basis of one-step methods. Explicit and diagonally implicit two-step methods with the second or third stage order are examined. Test problems are presented showing that the proposed methods are superior to conventional one-step techniques. 
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     author = {L. M. Skvortsov},
     title = {A~simple technique for constructing two-step {Runge{\textendash}Kutta} methods},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_11_a1/}
}
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L. M. Skvortsov. A simple technique for constructing two-step Runge–Kutta methods. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 11, pp. 1920-1930. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_11_a1/

[1] Jackiewich Z., Tracogna S., “A general class of two-step Runge-Kutta methods for ordinary differential equations”, SIAM J. Numer. Analys, 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. Analys, 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] Jackiewicz Z., Verner J. H., “Derivation and implementation of two-step Runge–Kutta pairs”, Japan J. Ind. Appl. Math., 19 (2002), 227–248 | DOI | MR | Zbl

[7] Chollom J., Jackiewicz Z., “Construction of two-step Runge–Kutta methods with large regions of absolute stability”, J. Comput. Appl. Math., 157:1 (2003), 125–137 | DOI | MR | Zbl

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

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

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

[11] Kværnø A., “Singly diagonally implicit Runge–Kutta methods with an explicit first stage”, BIT, 44:3 (2004), 489–502 | DOI | MR | Zbl

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

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

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

[15] Jay L., “Convergence of a class of Runge–Kutta methods for differential-algebraic systems of index 2”, BIT, 33:1 (1993), 137–150 | DOI | MR | Zbl