Geodesic
Variable order and step integrating algorithm based on the explicit two-stage Runge–Kutta method
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 10 (2007) no. 2, pp. 177-185 Cet article a éte moissonné depuis la source Math-Net.Ru

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The inequality for a stability control of the explicit two-stage Runge–Kutta like method is obtained.With the usage of stages of this scheme, the methods of first and second order are developed.The method of first order has a maximal length of the stability interval equal to 8. The algorithm of variable order and step is created, for which the most efficient computational scheme is chosen from the stability criterion. Numerical results with an additional stability control and variable order demonstrate an increase in efficiency. 
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     author = {L. V. Knaub and Yu. M. Laevsky and E. A. Novikov},
     title = {Variable order and step integrating algorithm based on the explicit two-stage {Runge{\textendash}Kutta} method},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
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L. V. Knaub; Yu. M. Laevsky; E. A. Novikov. Variable order and step integrating algorithm based on the explicit two-stage Runge–Kutta method. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 10 (2007) no. 2, pp. 177-185. http://geodesic.mathdoc.fr/item/SJVM_2007_10_2_a4/

[1] Shampine L. M., “Implementation of Rosenbrok method”, ACM Transaction on Mathematical Software, 8:5 (1982), 93–113 | DOI | MR | Zbl

[2] Novikov E. A., Novikov V. A., “Kontrol ustoichivosti yavnykh odnoshagovykh metodov integrirovaniya obyknovennykh differentsialnykh uravnenii”, DAN SSSR, 277:5 (1984), 1058–1062 | MR | Zbl

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

[4] Fehlberg E., “Classical fifth-, sixth-, seventh- and eighth order Runge–Kutta formulas with step size control”, Computing, 4 (1969), 93–106 | DOI | MR | Zbl

[5] Eright W. H., Hull T. E., “Comparing numerical methods for the solutions of systems of ODE's”, BIT Numerical Mathematics, 15:1 (1975), 10–48 | DOI