Mathematical modeling and simulations using software like MATLAB, COMSOL and Python

This study explores the application of MATLAB, COMSOL, and Python in mathematical modeling and simulation within precision engineering. These tools are analyzed for their strengths in handling various engineering challenges, from control systems to multiphysics simulations and custom algorithm development. The study also investigates the role of artificial intelligence (AI), in supporting mathematical modeling tasks by automating coding, providing concept explanations, and aiding model structuring. By comparing computational performance, accuracy, and usability, the research aims to identify the best-suited software for different simulation types, such as thermal-fluid dynamics and structural analysis. The findings underscore the significance of choosing appropriate software for optimizing computational resources, validating models, and achieving reliable, efficient simulations. This study contributes practical guidelines for bridging the gap between theoretical models and practical applications, enhancing productivity, and fostering innovation in precision engineering.