Basic methods of mathematical modeling
Mechanism analysis: according to the understanding of the characteristics of objective things, find out the quantitative law reflecting the internal mechanism
Test analysis: treat the object as a "black box", and find the model that best fits the data through statistical analysis of the measurement data
Combination of the two: use mechanism analysis to establish the model structure, and use test analysis to determine the model parameters (mechanism analysis does not have a unified method, mainly through case studies (Case Studies) to learn. The following modeling mainly refers to mechanism analysis.
Specific steps to establish a mathematical model
First, model preparation
First of all, we must understand the actual background of the problem, clarify the purpose of modeling, collect all necessary information, and try to figure out the characteristics of the object.
Second, model assumptions
According to the characteristics of the object and the purpose of modeling, the necessary and reasonable simplification of the problem and the use of precise language to make assumptions are a crucial step in modeling. If you consider all the factors of the problem, it is undoubtedly a courageous but poorly approached behavior. Therefore, a superb modeler can give full play to imagination, insight and judgment, and is good at distinguishing priority and in order to make the processing method. Simple, try to make the problem linear and uniform.
Third, the model composition
Analyze the causality of the object based on the hypothesis made&#x