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This article is cited in 2 scientific papers (total in 2 papers)
Applied mathematics
Two-parametric family of sixth order numerical methods for solving systems of ordinary differential equations
I. V. Olemskoy, N. A. Kovrizhnykh, O. S. Firyulina St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
Abstract:
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.
Received: November 2, 2019 Accepted: November 7, 2019
Citation:
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 S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 15:4 (2019), 502–517
Linking options:
https://www.mathnet.ru/eng/vspui424 https://www.mathnet.ru/eng/vspui/v15/i4/p502
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Abstract page: | 103 | Full-text PDF : | 22 | References: | 19 | First page: | 3 |
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