This article is cited in 7 papers

A nonlocal problem for singular linear systems of ordinary differential equations

A. A. Abramov^a, V. I. Ul'yanova^a, L. F. Yukhno<sup>b

a</sup> Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333 Russia
^b Institute of Mathematical Modeling, Russian Academy of Sciences, Miusskaya pl. 4a, Moscow, 125047 Russia

Abstract: A system of linear ordinary differential equations is examined on an infinite half-interval. This system is supplemented by the boundedness condition for solutions and a nonlocal linear condition specified by the Stieltjes integral. A method for approximating the resulting problem by a problem posed on a finite interval is proposed, and the properties of the latter are investigated. A numerically stable method for solving this problem is examined. This method uses an auxiliary boundary value problem with separated boundary conditions.

Key words: singular system of ordinary differential equations, nonlocal condition, numerical method.

UDC: 519.622.2

Received: 18.10.2010

 English version: Computational Mathematics and Mathematical Physics, 2011, 51:7, 1146–1152

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