Method of establishing mathematical model

Generally speaking, the methods of establishing mathematical models can be divided into two categories, one is mechanism analysis and the other is experimental analysis. Mechanism analysis is based on the understanding of the characteristics of real objects, to find out the laws reflecting the internal mechanism and analyze its causal relationship-the established models often have clear physical or practical significance.

Model preparation

First of all, we should understand the actual background of the problem, clarify the purpose of modeling, and collect all kinds of information necessary for modeling, such as phenomena and data. And try to clarify the characteristics of the object, so as to initially determine which model to use. In short, we should be prepared for modeling.

Model hypothesis

According to the characteristics of the object and the purpose of modeling, it is a key step to simplify the problem and make assumptions with accurate language. Different simplified assumptions will lead to different models.

Model composition

According to the assumptions made, the causal relationship of the object is analyzed, and the equation (or inequality) relationship between various quantities (constants and variables) or other mathematical structures are constructed by using the internal laws of the object and appropriate mathematical tools.

Model solving

We can use all kinds of traditional and modern mathematical methods, especially computer technology, such as solving equations, drawing pictures, proving theorems, logical operations, numerical calculation and so on.