1, model preparation: understand the actual background of the problem, clarify its practical significance, and master all kinds of information of the object. Describe the problem in mathematical language.
2. Model hypothesis: according to the characteristics of the actual object and the purpose of modeling, simplify the problem and put forward some appropriate assumptions in accurate language.
3. Modeling: On the basis of assumptions, use appropriate mathematical tools to describe the mathematical relationship between variables and establish the corresponding mathematical structure.
4. Model solution: calculate (estimate) all parameters of the model by using the obtained data. Model analysis: analyze the results by mathematical methods.
5. Model test: compare the results of model analysis with the actual situation to verify the accuracy, rationality and applicability of the model. If the model is in good agreement with the actual situation, the practical significance of the calculation results should be given and explained. If the model is not consistent with the actual situation, it is necessary to modify the assumptions and repeat the modeling process. Model application: the application method varies with the nature of the problem and the purpose of modeling.
Extended data:
Mathematical modeling is a mathematical thinking method, and it is a powerful mathematical means to describe and "solve" practical problems by using mathematical language and methods through abstraction and simplification.
Mathematical modeling is a process of describing actual phenomena with mathematical language. The actual phenomena here include both concrete natural phenomena, such as free fall, and abstract phenomena, such as customers' value tendency to a certain commodity. The description here includes not only the description of external form and internal mechanism, but also the prediction, experiment and explanation of actual phenomena.
We can also intuitively understand this concept: mathematical modeling is a process that makes pure mathematicians (mathematicians who only study mathematics and don't care about its application in practice) become physicists, biologists, economists and even psychologists.