Two-parametric family of sixth order numerical methods for solving systems of ordinary differential equations

被引：2
|
作者：
Olemskoy, I., V [1 ]
Kovrizhnykh, N. A. [1 ]
Firyulina, O. S. [1 ]
机构：
[1] St Petersburg State Univ, 7-9 Univ Skaya Nab, St Petersburg 199034, Russia
来源：
VESTNIK SANKT-PETERBURGSKOGO UNIVERSITETA SERIYA 10 PRIKLADNAYA MATEMATIKA INFORMATIKA PROTSESSY UPRAVLENIYA | 2019年 / 15卷 / 04期
关键词：
order; the order conditions; simplifying conditions;
D O I：
10.21638/11702/spbu10.2019.407
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：502 / 517
页数：16
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