Construction of discrete analogue of the differential operator $\frac{d^4}{d{x}^4}+2\frac{d^2}{d{x}^2}+1$ and its properties

In the present paper the discrete analogue of the differential operator $\frac{d^4}{d{x}^4}+2\frac{d^2}{d{x}^2}+1$ is constructed and its some properties are proved.