Geodesic
Two-parametric family of sixth order numerical methods for solving systems of ordinary differential equations
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 15 (2019) no. 4, pp. 502-517 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper is devoted to the construction of economical explicit sixth-order numerical method for solving structurally partitioned systems of ordinary differential equations. The general form of the method, which algorithmically uses the properties of the system structure, is presented. Conditions of order six, which the parameters of the method must satisfy, are derived. The simplifying conditions are found, which reduces the large nonlinear system of order conditions to a solvable smaller system. A solution with two free parameters is obtained. Economic explicit sixth-order schemes for systems of ordinary differential equations are presented. Numerical tests to compare to known explicit sixth-order one-step methods are performed.
Keywords: order, the order conditions, simplifying conditions. 
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I. V. Olemskoy; N. A. Kovrizhnykh; O. S. Firyulina. Two-parametric family of sixth order numerical methods for solving systems of ordinary differential equations. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 15 (2019) no. 4, pp. 502-517. http://geodesic.mathdoc.fr/item/VSPUI_2019_15_4_a6/

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