Dynamic Behavior Modeling of Information Technology Systems Using Differential Equations

Abstract

This research aims to analyze the advanced role played by differential equations in improving the modeling of modern information systems and technologies, in light of the increasing shift toward complex dynamic systems characterized by continuous change and nonlinearity. The research problem arises from the limitations of traditional static models in accurately describing the real performance of digital systems such as computer networks, servers, and artificial intelligence applications, which are influenced by multiple temporal and interactive factors. The study adopts an analytical approach to examine the theoretical foundations of differential equations, along with a numerical approach for applying approximate solution methods. These models are employed in applied cases that reflect real-world information technology systems. The results show that the use of differential equations significantly improves modeling accuracy, enhances predictive capability, and supports more efficient technical decision-making compared to traditional models