2. Model assumptions. On the basis of clarifying the modeling purpose and mastering the necessary data, the main influencing factors are found out through the analysis and calculation of the data. After necessary refinement and simplification, some assumptions that conform to the objective reality are put forward, thus highlighting the main characteristics of the problem and ignoring the secondary aspects of the problem. Generally speaking, it is difficult to turn a practical problem into a mathematical problem without simplifying the hypothesis, and even if it is possible, it is difficult to solve it. Different simplified assumptions will lead to different models. Unreasonable or oversimplified assumptions will lead to model failure or partial failure, so the assumptions should be revised and supplemented. If the assumptions are too detailed, trying to take all the factors of complex objects into account may make it difficult or even impossible for you to continue your next work. Usually, the basis of making assumptions is based on the understanding of the inherent law of the problem, the analysis of data or phenomena, or the combination of the two. When making assumptions, we should not only use the knowledge of physics, chemistry, biology and economy related to the problem, but also give full play to our imagination, insight and judgment. We should be good at distinguishing the primary and secondary problems, firmly grasp the main factors, abandon the secondary factors, and linearize and homogenize the problems as much as possible. Experience often plays an important role here. When writing assumptions, the language should be accurate, just like writing known conditions when doing exercises.
3. Model composition. According to the assumptions made and the relationship between things, the relationship between variables is described with appropriate mathematical tools, and the corresponding mathematical structure-that is, the mathematical model is established. Turn the problem into a mathematical problem. We should pay attention to using simple mathematical tools as much as possible, because simple mathematical models can often better reflect the essence of things and are easy to be mastered and used by more people.
4. Model solving. Using known mathematical methods to solve the mathematical problems obtained in the previous step often requires further simplification or hypothesis. When it is difficult to get an analytical solution, we should also get a numerical solution with the help of a computer.
5. Model analysis. Mathematically analyzing the solution of the model, sometimes it is necessary to analyze the dependence or stability of variables according to the nature of the problem, sometimes it is necessary to give a mathematical prediction according to the obtained results, and sometimes it is possible to give a mathematical optimal decision or control. In either case, it is usually necessary to analyze the error, the stability or sensitivity of the model to the data and so on.
6. Model check. Analyze the practical significance of the results and compare them with the actual situation to see if they are in line with the reality. If the results are not satisfactory, some models must be modified, supplemented with assumptions or re-modeled, and some models need to be repeated several times and constantly improved.
7. Model application. The established model must be applied in practice to produce benefits, and it is constantly improved and perfected in application. The way of application naturally depends on the nature of the problem and the purpose of modeling.