A. A. Abramov, L. F. Yukhno, “A nonlinear singular eigenvalue problem for a linear system of ordinary differential equations with redundant conditions”, Zh. Vychisl. Mat. Mat. Fiz., 2016, Volume 56, Number 7,Pages <nobr>1294

This article is cited in 1 paper

A nonlinear singular eigenvalue problem for a linear system of ordinary differential equations with redundant conditions

A. A. Abramov^a, L. F. Yukhno^bc

^a Dorodnicyn Computing Center, Russian Academy of Sciences
^b National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
^c Institute of Applied Mathematics, Russian Academy of Sciences

Abstract: A nonlinear eigenvalue problem for a linear system of ordinary differential equations is examined on a semi-infinite interval. The problem is supplemented by nonlocal conditions specified by a Stieltjes integral. At infinity, the solution must be bounded. In addition to these basic conditions, the solution must satisfy certain redundant conditions, which are also nonlocal. A numerically stable method for solving such a singular overdetermined eigenvalue problem is proposed and analyzed. The essence of the method is that this overdetermined problem is replaced by an auxiliary problem consistent with all the above conditions.

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

UDC: 519.622.2

Received: 26.01.2016

DOI: 10.7868/S0044466916070024