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# Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

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Volume 18, Issue 4

# Computation of Green’s Function of the Bounded Solutions Problem

Vitalii G. Kurbatov
• Corresponding author
• Department of Mathematical Physics, Voronezh State University, 1 Universitetskaya Square, Voronezh 394018, Russia
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• Other articles by this author:
/ Irina V. Kurbatova
• Department of Software Development and Information Systems Administration, Voronezh State University, 1 Universitetskaya Square, Voronezh 394018, Russia
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Published Online: 2017-10-12 | DOI: https://doi.org/10.1515/cmam-2017-0042

## Abstract

It is well known that the equation ${x}^{\prime }\left(t\right)=Ax\left(t\right)+f\left(t\right)$, where A is a square matrix, has a unique bounded solution x for any bounded continuous free term f, provided the coefficient A has no eigenvalues on the imaginary axis. This solution can be represented in the form

$x\left(t\right)={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\mathcal{𝒢}\left(t-s\right)f\left(s\right)𝑑s.$

The kernel $\mathcal{𝒢}$ is called Green’s function. In this paper, for approximate calculation of $\mathcal{𝒢}$, the Newton interpolating polynomial of a special function ${g}_{t}$ is used. An estimate of the sensitivity of the problem is given. The results of numerical experiments are presented.

MSC 2010: 65F60; 65D05; 34B27; 34B40; 34D09

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Revised: 2017-09-12

Accepted: 2017-09-15

Published Online: 2017-10-12

Published in Print: 2018-10-01

Funding Source: Ministry of Education and Science of the Russian Federation

Award identifier / Grant number: 3.1761.2017/4.6

Funding Source: Russian Foundation for Basic Research

Award identifier / Grant number: 16-01-00197

The first author was supported by the Ministry of Education and Science of the Russian Federation under state order no. 3.1761.2017/4.6. The second author was supported by the Russian Foundation for Basic Research under research project no. 16-01-00197.

Citation Information: Computational Methods in Applied Mathematics, Volume 18, Issue 4, Pages 673–685, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840,

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