Geodesic
A fifth-order five-stage embedded method of the Dormand–Prince type
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 7, pp. 1181-1191 Cet article a éte moissonné depuis la source Math-Net.Ru

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An explicit embedded method is examined for the numerical integration of a system of ordinary differential equations of a special form. Fifth-order five-stage numerical schemes with automatic step size selection are constructed for special systems of differential equations of the first and second orders. 
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I. V. Olemskoi. A fifth-order five-stage embedded method of the Dormand–Prince type. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 7, pp. 1181-1191. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_7_a4/

[1] Olemskoi I. V., “Chislennyi metod integrirovaniya sistem obyknovennykh differentsialnykh uravnenii”, Matem. metody analiza upravlyaemykh protsessov, L., 1986, 157–160 | MR

[2] Olemskoi I. V., “Ekonomichnaya raschetnaya skhema chetvertogo poryadka tochnosti chislennogo integrirovaniya sistem spetsialnogo vida”, Protsessy upravleniya i ustoichivost, Tr. XXX nauchn. konf., NII Khimii SPbGU, SPb., 1999, 134–143

[3] Olemskoi I. V., “Strukturnyi podkhod v zadache konstruirovaniya yavnykh odnoshagovykh metodov”, Zh. vychisl. matem. i matem. fiz., 43:7 (2003), 961–974 | MR | Zbl

[4] Olemskoi I. V., “Chetyrekhetapnyi metod pyatogo poryadka tochnosti chislennogo integrirovaniya sistem spetsialnogo vida”, Zh. vychisl. matem. i matem. fiz., 42:8 (2002), 1179–1190 | MR | Zbl

[5] Olemskoi I. V., “Metody tipa Runge-Kutty integrirovaniya sistem i differentsialnykh uravnenii vtorogo poryadka spetsialnogo vida”, Vychisl. tekhnologii, 9:2 (2004), 67–81 | Zbl

[6] Dormand J. R., Prince P. J., “New Runge-Kutta algorithms for numerical simulation in dynamical astronomy”, Celestial Mech., 18 (1978), 223–232 | DOI | MR | Zbl

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

[8] Dormand J. R., El-Mikkawy M. E. A., Prince P. J., “Families of Runge-Kutta-Nystrom formulae”, J. Numer. Analys., 7 (1987), 235–250 | DOI | MR | Zbl

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

[10] Arushanyan O. B., Zaletkin S. F., Chislennoe reshenie obyknovennykh differentsialnykh uravnenii na Fortrane, Izd-vo MGU, M., 1990 | MR | Zbl

[11] Olemskoi I. V., “Algoritm vydeleniya strukturnykh osobennostei”, Nikolai Efimovich Kirin, ASSPIN, SPb., 2003, 234–251