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Methods and steps of establishing mathematical model?
First, the model preparation should first understand the actual background of the problem, clarify the modeling purpose, collect all kinds of necessary information, and try to understand the characteristics of the object. 2. Model Hypothesis According to the characteristics of the object and the purpose of modeling, it is a crucial step to simplify the problem reasonably and make assumptions in accurate language. If all the factors of the problem are taken into account, it is undoubtedly a courageous act and the method is very poor. Therefore, a superb modeler can give full play to his imagination, insight and judgment, be good at distinguishing priorities, and linearize and homogenize problems as much as possible in order to simplify the handling methods. Thirdly, according to the assumptions made, the model structure analyzes the causal relationship of the object, and constructs the equation relationship between various quantities or other mathematical structures by using the internal laws of the object and appropriate mathematical tools. At this time, we will enter a vast world of applied mathematics, where there are many lovely children at the knees of the elderly with high numbers and probabilities. They are graph theory, queuing theory, linear programming, game theory and many other theories. They are really a great country with unique views. But we should remember that the mathematical model is established for more people to understand and apply, so the simpler the tool, the more valuable it is. Fourthly, the model can be solved by various traditional and modern mathematical methods, especially computer technology, such as solving equations, drawing, proving theorems, logical operations, numerical operations and so on. Solving a practical problem often requires complicated calculation, and in many cases, the system operation has to be simulated by computer, so programming ability and familiarity with mathematical software packages are very important. Fifthly, the model analysis makes a mathematical analysis of the model solution. Looking horizontally, the side of the ridge has become a peak with different heights. Whether you can analyze the model results carefully and accurately determines whether your model can reach a higher level. Also remember that in either case, error analysis and data stability analysis are needed.