This article is cited in 12 papers

Solving a system of linear ordinary differential equations with redundant conditions

A. A. Abramov^ab, L. F. Yukhno<sup>cd

a</sup> Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia (MFTI)
^b Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia
^c Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4a, Moscow, 125047, Russia
^d Moscow Engineering Physics Institute (State University), Kashirskoe sh. 31, Moscow, 115409, Russia (MIFI)

Abstract: A system of linear ordinary differential equations is examined under the assumption that, in addition to the basic conditions, which in general are nonlocal and are specified by a Stieltjes integral, certain redundant (and possibly also nonlocal) conditions are imposed. Generically, such a problem has no solution. A principle for constructing an auxiliary system is proposed. This system replaces the original one and is normally consistent with all the conditions prescribed. A method for solving this auxiliary problem is analyzed. The method is numerically stable if the auxiliary problem is numerically stable.

Key words: linear system of ordinary differential equations, redundant nonlocal conditions, numerical stability.

UDC: 519.622.2

Received: 10.11.2013

DOI: 10.7868/S0044466914040024

 English version: Computational Mathematics and Mathematical Physics, 2014, 54:4, 598–603

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