Geodesic
Model equations for accuracy investigation of Runge--Kutta methods
Matematičeskoe modelirovanie, Tome 22 (2010) no. 5, pp. 146-160.

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

The simplest equations are considered that simulate the behavior of various error components of Runge–Kutta methods. The expressions for the local and global errors are obtained. The minimization of these errors allows one to construct explicit and implicit methods that have an improved accuracy when solving stiff and differential-algebraic problems.
Keywords: Runge–Kutta methods, still problems, differential-algebraic problems, order reduction phenomen. 
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L. M. Skvortsov. Model equations for accuracy investigation of Runge--Kutta methods. Matematičeskoe modelirovanie, Tome 22 (2010) no. 5, pp. 146-160. http://geodesic.mathdoc.fr/item/MM_2010_22_5_a13/

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

[2] Prothero A., Robinson A., “On the stability and accuracy of one-step methods for solving stiff systems of ordinary differential equations”, Mathematics of Computations, 28:1 (1974), 145–162 | DOI | MR

[3] Dekker K., Verver Ya., Ustoichivost metodov Runge-Kutty dlya zhestkikh nelineinykh differentsialnykh uravnenii, Mir, M., 1988, 334 pp. | MR

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

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

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

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

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

[9] Kalitkin N. N., “Chislennye metody resheniya zhestkikh sistem”, Matem. modelirovanie, 7:5 (1995), 8–11 | Zbl

[10] Cameron F., Palmroth M., Piche R., “Quasi stage order conditions for SDIRK methods”, Appl. Numer. Math., 42:1–3 (2002), 61–75 | DOI | MR | Zbl

[11] Jay L., “Convergence of Runge-Kutta methods for differential-algebraic systems of index 3”, Appl. Numer. Math, 17:2 (1995), 97–118 | DOI | MR | Zbl

[12] 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