Numerical solution of a differential equation with a lagging argument

Systems of equations with delay are widely used in various fields of modern mathematical modeling. The development and implementation of effective algorithms for the numerical solution of various classes of equations with lagging arguments is an urgent task. In this article, we considered the modeling of the learning process, which are described by classes of differential equations with a lagging argument. When developing the structure of a mathematical model, it is necessary to apply the modified Runge-Kutta method, which allows for integration with a variable step and localize the points of discontinuity of derivatives. The application of sequential integration methods (step-by-step method) for solving a differential equation with a lagging argument and comparing the resulting solution with numerical methods using the Matlab software package is considered.