Geodesic
A family of sixth-order methods with six stages
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 14 (2018) no. 3, pp. 215-229

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The paper deals with construction of an efficient explicit sixth order method for structurally partitioned systems of ordinary differential equations. The general scheme of the method is presented, which algorithmically uses structural properties of a system of differential equations. The order conditions and the simplifying conditions for the considered explicit six-stage method are written down and their consistency is determined. The general solution with seven free parameters is obtained and a computational scheme for certain values of free parameters is constructed. Its performance on test problems is compared to three other explicit sixth-order methods.
Keywords: order, order conditions, simplifying conditions. 
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     author = {I. V. Olemskoy and N. A. Kovrizhnykh},
     title = {A family of sixth-order methods with six stages},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
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     volume = {14},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2018_14_3_a2/}
}
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I. V. Olemskoy; N. A. Kovrizhnykh. A family of sixth-order methods with six stages. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 14 (2018) no. 3, pp. 215-229. http://geodesic.mathdoc.fr/item/VSPUI_2018_14_3_a2/