This article is cited in 2 papers

Solving some problems for systems of linear ordinary differential equations with redundant conditions

A. A. Abramov^a, L. F. Yukhno<sup>b

a</sup> 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.

UDC: 519.62

Received: 15.09.2016

DOI: 10.7868/S0044466917080026

 English version: Computational Mathematics and Mathematical Physics, 2017, 57:8, 1277–1284

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