Numerical methods for solving boundary value problems for linear first kind second order differential equations with deviating argument on balanced segment

In the developed numerical method for solving the first boundary value problem for a model second-order ordinary differential equation with deviating argument. Built finite-difference scheme that approximates the differential problem with the accuracy of second order in step a uniform grid. From the resulting a priori estimates of the solution finite difference scheme implies its convergence under certain conditions to the input parameters of the problem. The method of implementation of the finite scheme consisting in the presentation of its solutions in the form of a sum of two grid functions, each of which is a solution of the classical boundary value problem for a differential equation of second order. Conducted computing experiments confirm the theoretical results obtained in this work. The work is an example of the problem, which has countless solutions due to violations of the conditions for its unique solvability.