Numerical analysis of multicomponent dynamic models of stage-by-stage knowledge assimilation

The development of models that make it possible to study the dynamics of knowledge assimilation in an educational environment and evaluate the effectiveness of knowledge retention is one of the topical research tasks. In educational systems it is not always possible to optimize the learning process in such a way that knowledge is reliably retained and not forgotten in the short term. The construction, as well as analytical and numerical study of mathematical models to describe the processes of knowledge accumulation and assimilation is aimed at creating effective tools for improving the elements of learning systems and educational technologies. The aim of the study is to perform a computerized investigation of multicomponent models of step-by-step knowledge assimilation described by finite-dimensional systems of ordinary differential equations using the Python programming language. We study multicomponent models of knowledge assimilation describing transitions between different levels of knowledge strength, from quickly forgotten to the most stable. The models are specified using finite-dimensional systems of ordinary differential equations, whose parameters allow us to control the process of knowledge distribution by levels and analyze the dynamics characteristic of the knowledge assimilation process. Cases with different number of knowledge strength levels are considered, phase trajectories are visualized and solutions are analyzed for given sets of parameters. The obtained results can be used in the tasks of computer research of multicomponent dynamic models, mathematical modeling of pedagogical processes, optimization of the learning process.