Explicit Runge–Kutta methods for moderately stiff problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 11, pp. 2017-2030
L. M. Skvortsov. Explicit Runge–Kutta methods for moderately stiff problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 11, pp. 2017-2030. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_11_a9/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Explicit Runge–Kutta methods (including stabilized methods) possessing improved accuracy when solving moderately stiff problems are considered. The advantages of the new methods over the ordinary ones are demonstrated.

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

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

[3] Skvortsov L. M., “O povyshenii tochnosti yavnykh metodov Runge-Kutty pri reshenii umerenno zhestkikh zadach”, Dokl. RAN, 378:5 (2001), 602–604 | MR | Zbl

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

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

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

[7] Shampine L. F., Reichelt M. W., “The MATLAB ODE suite”, SIAM J. Sci. Comput., 18:1 (1997), 1–22 | DOI | MR | Zbl

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

[9] 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

[10] Lebedev V. I., “Yavnye raznostnye skhemy dlya resheniya zhestkikh zadach s kompleksnym ili razdelimym spektrom”, Zh. vychisl. matem. i matem. fiz., 40:12 (2000), 1801–1812 | Zbl

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

[12] Medovikov A. A., “Third order explicit method for the stiff ordinary differential equations”, Numer. Analys. and its Applic., Lect. Notes in Comput. Sci., 1196, Springer, 1997, 327–334 | MR