A. A. Abramov, L. F. Yukhno, “Solving a singular nonlocal problem with redundant conditions for a system of linear ordinary differential equations”, Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 3,Pages <nobr>385

This article is cited in 5 papers

Solving a singular nonlocal problem with redundant conditions for a system of linear ordinary differential equations

A. A. Abramov^ab, L. F. Yukhno^cd

^a Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia (MFTI)
^b Dorodnicyn Computing Center, Federal Research Center "Computer Science and Control" of 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 National Research Nuclear University (Moscow Engineering Physics Institute, MEPHI), Kashirskoe sh. 31, Moscow, 115409, Russia

Abstract: A system of linear ordinary differential equations is examined on an infinite or semi-infinite interval. The basic conditions are nonlocal and are specified by a Stieltjes integral; moreover, certain redundant (and also nonlocal) conditions are imposed. At infinity, the solution is required to be bounded. A method for solving such an over-determined problem is proposed and analyzed. The method is numerically stable if an auxiliary problem that replaces the original one is numerically stable.

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

UDC: 519.624

MSC: Primary 34A45; Secondary 65L05, 65L20

Received: 06.10.2014

DOI: 10.7868/S0044466915030023