Geodesic
Families of embedded methods of order six
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 18 (2022) no. 2, pp. 285-296

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In the paper embedded methods of order six, with seven stages for solving systems of ordinary differential equations, are derived. A family of Runge — Kutta methods, of order six with seven stages and having three free parameters, is presented. This family is extended in two different ways with embedded methods to form families of embedded method pairs. Numerical comparison is given for certain examples of the embedded pairs from the constructed families.
Keywords: Cauchy problem, embedded methods, error control, order, stage, order conditions, simplifying conditions. 
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     author = {I. V. Olemskoy and O. S. Firyulina and O. A. Tumka},
     title = {Families of embedded methods of order six},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {285--296},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2022_18_2_a8/}
}
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I. V. Olemskoy; O. S. Firyulina; O. A. Tumka. Families of embedded methods of order six. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 18 (2022) no. 2, pp. 285-296. http://geodesic.mathdoc.fr/item/VSPUI_2022_18_2_a8/