It is well known that the equation $x(t)=Ax(t)+f(t)$, 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 Greens function. In the paper, a representation of Greens 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.
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