The connection between the stochastic series and the time depending phenomena

The present paper employs computer-assisted methods in order to solve different type of equations and systems.The most significant goal is to transform, by modeling, time-depending series, such as stochastic series forinstance, into dynamic systems that can be solved, while also obtaining visual representations of their solutions.So, we have started with an introduction including different computer-assisted methods for solving differentialequations and systems, followed by a proposed algorithm that leads to both an analytical formula and a graphicalrepresentation of the optimal solution and command for a specific class of dynamical systems.Through this work, we have shown that stochastic series can be expressed, through mathematical modeling, as atime-dependent system of equations or even as dynamic system, which we have established an obvious similaritywith the generalised dynamic systems of the age-structured populations, discovered by J.R. Chasnov.The connection which we have established allows for the application of the classical computer-assisted methods,as well as particular algorithms, for many other time-dependent series, which can be modeled in the dynamicsystem form, particularly when the main term follows a time-recurring formula.