Geodesic
Optimal first- to sixth-order accurate Runge–Kutta schemes
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 3, pp. 418-429 
E. A. Alshina; E. M. Zaks; N. N. Kalitkin. Optimal first- to sixth-order accurate Runge–Kutta schemes. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 3, pp. 418-429. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_3_a5/
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     title = {Optimal first- to sixth-order accurate {Runge{\textendash}Kutta} schemes},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_3_a5/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

An optimal choice of free parameters in explicit Runge–Kutta schemes up to the sixth order is discussed. A sixth-order seven-stage scheme that is immediately ahead of Butcher's second barrier is constructed. The study is performed in the most general form, and its results are applicable to both autonomous and nonautonomous problems.

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