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This article is cited in 2 scientific papers (total in 2 papers)
Solving some problems for systems of linear ordinary differential equations with redundant conditions
A. A. Abramova, L. F. Yukhnob a Dorodnitsyn Computing Center, Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, Moscow, Russia
b Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia
Abstract:
Numerical methods are proposed for solving some problems for a system of linear ordinary differential equations in which the basic conditions (which are generally nonlocal ones specified by a Stieltjes integral) are supplemented with redundant (possibly nonlocal) conditions. The system of equations is considered on a finite or infinite interval. The problem of solving the inhomogeneous system of equations and a nonlinear eigenvalue problem are considered. Additionally, the special case of a self-adjoint eigenvalue problem for a Hamiltonian system is addressed. In the general case, these problems have no solutions. A principle for constructing an auxiliary system that replaces the original one and is normally consistent with all specified conditions is proposed. For each problem, a numerical method for solving the corresponding auxiliary problem is described. The method is numerically stable if so is the constructed auxiliary problem.
Key words:
system of ordinary differential equations, nonlocal additional conditions, redundant conditions, nonlinear eigenvalue problem, numerical stability.
Received: 15.09.2016
Citation:
A. A. Abramov, L. F. Yukhno, “Solving some problems for systems of linear ordinary differential equations with redundant conditions”, Zh. Vychisl. Mat. Mat. Fiz., 57:8 (2017), 1285–1293; Comput. Math. Math. Phys., 57:8 (2017), 1277–1284
Linking options:
https://www.mathnet.ru/eng/zvmmf10599 https://www.mathnet.ru/eng/zvmmf/v57/i8/p1285
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Abstract page: | 194 | Full-text PDF : | 19 | References: | 45 | First page: | 7 |
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