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Abstract
This study explores how mathematical techniques can be effectively combined with computer-based modeling and simulation to solve real-world problems in science, engineering, and social systems. The research focuses on understanding the role of mathematical models in predicting complex behaviours and improving decision-making. Previous studies have shown that mathematical modeling enhances the accuracy and efficiency of simulations, but there is still a need to integrate these methods in a more systematic way. The main purpose of this paper is to demonstrate how various mathematical tools, such as differential equations, optimization, and statistical analysis, can be used to design accurate and reliable simulation models. For this study, several case-based simulations were developed using numerical and statistical methods, and the results were compared using standard performance indicators. All experiments were carried out using computer modeling software with clearly defined parameters and controlled variables. The findings showed that integrating mathematical techniques significantly improved model accuracy, reduced computation time, and provided better insights into system behavior. The results also agreed with existing research, supporting the reliability of this approach. In conclusion, the study proves that combining mathematics with computer-based simulations creates a powerful framework for analyzing and solving practical problems in diverse fields, making it a valuable approach for future technological and scientific development.
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