Predicting stock price and exchange rate fluctuations is a key issue for economic actors, investors, and policymakers. Although time series statistical methods have been widely used in this field, these methods face limitations such as simplifying assumptions and reduced accuracy in complex conditions. In this study, the ability of modern numerical methods, especially the drop motion algorithm, in predicting stock price fluctuations was investigated and compared with time series statistical methods. First, a comprehensive review of the literature related to new numerical methods was conducted, and then the drop motion algorithm was implemented on the Tehran Stock Exchange stock price index data. The results of the analysis showed that this algorithm performs better than time series methods in predicting fluctuations, especially in conditions of nonlinear and complex fluctuations, and significantly increases the prediction accuracy. Also, this method showed greater ability in identifying short-term market trends. The findings indicate the high potential of numerical methods in predicting financial fluctuations and it is suggested that these methods be investigated in other economic and financial fields as well. This research, by presenting a new approach to the field of financial forecasts, suggests the use of numerical methods as a complementary tool for financial analyses.