Ознака даламбера в контексті сучасного математичного моделювання

Abstract

The paper conducts a comprehensive analysis of the applied significance of D'Alembert's ratio test in the context of modern mathematical modeling and computational sciences. The mechanism of using this criterion for diagnosing the stability of dynamic systems and predicting the convergence of iterative processes is investigated. Special attention is paid to the method's efficiency when dealing with rapidly growing functions (factorials, exponentials), where it serves as a means of optimizing computational resources. The role of the test as a tool for algorithm verification in information technology and engineering calculations is substantiated.