1. model preparation, first of all, we should understand the actual background of the problem, clarify the purpose of modeling, and collect necessary information such as phenomena and data. And try to find out the main characteristics of the object to form a clear "problem", so as to initially determine which model to use.

2. Model hypothesis, according to the characteristics of the object and the purpose of modeling, grasp the essence of the problem, ignore the secondary factors, and simplify the hypothesis necessary and reasonable. This is a very important and difficult step in modeling success or failure.

If the assumptions are unreasonable or simple, it will lead to wrong or useless models. If the assumption is too detailed, if you try to take all the rudder factors of complex objects into account, it will be difficult or impossible for you to continue the next work. It is often necessary to make an appropriate compromise between rationality and simplification.

3. Model composition: According to the assumptions made, the internal laws of the object are described by mathematical language and fuathao, and the resume contains mathematical models of constants and variables, such as optimization model, differential equation model, difference equation model and graph model.

In addition to the professional knowledge of some related disciplines, it is often necessary to widely apply mathematics, be good at exerting imagination and pay attention to the application of analogy.

Analyze the * * * relationship between the object and other familiar objects, and borrow the existing model. Another principle to follow when modeling is: try to use simple mathematical tools, because your model always wants more people to understand and use it, not just a few experts to appreciate it.

4. The model can be solved by solving equations, drawing, optimization methods, numerical calculation, statistical analysis and other mathematical methods, especially mathematical software and computer technology.

5. Model analysis carries out mathematical analysis on the solution results, such as error analysis, statistical analysis, sensitivity analysis of the model to data, and robustness analysis of assumptions.

6. Model checking, that is, the solutions and analysis results are transformed back to the actual problems, and compared with the actual phenomena and data to test the rationality and applicability of the model. If the results are inconsistent with the reality, there will often be problems in the model assumptions, which should be revised, supplemented and re-modeled.