We investigate the approximation of a delay element in $\mathbb{R}^n$  in the case of a discontinuous driving-point function. The algorithm of the approximation for a system of difference equations by a system of ordinary differential equations is substantiated.

[1] Repin Yu.M. On approximate replacement of systems with delay by ordinary differential equations // Applied Mathematics and Mechanics. - 1965. - 29, N2. - P.226-245.

[2] Yanushevsky R.T. Control of objects with delay. - M.: Nauka, 1978. - 416 p.

[3] Obolensky A.Yu., Chernetskaya L.N. On one method of studying functional-differential models in problems of electrodynamics // Elektr. modeling. - 1993. - 15,
N4. - P.8-13.

[4]  Piddubna L.A., Cherevko I.M. Approximation of systems of differential-difference equations by systems of ordinary differential equations / / Nonlinear oscillations. - 1999. - N1. - P.42-50.

[5] Cherevko I.M., Matviy O.V. On approximation of systems with delay and their stability // Nonlinear oscillations. - 2004. - T.7, N2. - P.208-216.

[6] Matviy O.V., Cherevko I.M. Approximation of systems of differential-difference and difference equations with many delays // Nauk. visnyk Chernivtsiy un-tu: 3b. nauk. pr. Vyp. 150. Mathematics. Chernivtsi: Ruta, 2002. - P.50-54.

[7] Natanson I.P. Theory of functions of a real variable. - M.: Nauka, 1974. - 480 p.

[8] Cherevko I. M. On the approximate replacement of difference and differential-difference equations by ordinary differential equations // Nauk. Visnyk Chernivtsi Univ.: 3b. nauk. pr. Vyp. 134. Mathematics. Chernivtsi: Ruta, 2002. P.107-111.