Computation of Green's function of the bounded solutions problem

Abstract

It is well known that the equation $x^{\prime }(t)=Ax(t)+f(t)$, 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 \begin{equation*} x(t)=\int_{-\infty}^{\infty}\mathcal G(t-s)x(s)\,ds. \end{equation*} The kernel $\mathcal{G}$ is called Green's function. In the paper, a representation of Green's function in the form of the Newton interpolating polynomial is used for approximate calculation of $\mathcal{G}$. An estimate of the sensitivity of the problem is given.

arXiv comment12 pages, 2 figures

Cited by in corpus (1)

• The Gelfand--Shilov type estimate for Green's function of the bounded solutions problem