Application of computational method for differential equations for constructing correlation models

The article explores the use of differential equations as an alternative to the traditional least squares method for constructing correlation models that describe relationships between socio-economic phenomena and various processes. The authors demonstrate, through specific examples, that the differential equation method can be widely applied across different scientific fields, including economics, medicine, and engineering, to model both functional and statistical relationships. The approach is shown to provide realistic and practical models, especially in cases where traditional econometric techniques may not be suitable. The paper details several scenarios, including linear, quadratic, exponential, and logarithmic dependencies, illustrating how differential equations can be constructed and solved analytically or approximately based on experimental or observational data. The results confirm the effectiveness of the proposed method in producing models that closely match actual data, thereby enhancing the reliability of forecasts and analyses in complex systems.