1.

The process of mathematical modeling is to express the actual problem into a mathematical problem with mathematical language, mathematical concepts and mathematical symbols after analysis, abstraction and generalization. What kind of problem is expressed depends on the thinker's intention to solve the problem.

2. Dimensional analysis method

Dimensional analysis is a method of establishing mathematical model in the field of physics, which was put forward in the early 20th century. Based on experience and experiments, it uses the dimensional homogeneity of physical laws to determine the relationship between physical quantities. It is a mathematical analysis method. Through dimensional analysis, we can correctly analyze the relationship between variables, simplify the experiment and facilitate the arrangement of results.

3. Difference method

The mathematical idea of difference method is to discretize the derivative in the control equation by using the difference quotient of function values on grid nodes instead of Taylor series expansion, so as to establish an equation group with the values on grid nodes as unknowns, and transform the differential problem into an algebraic problem, which is an effective method to establish the mathematical model of discrete dynamic systems.

4. Variational method

Variational method is a mathematical field dealing with functions of functions, that is, functional problems, as opposed to ordinary calculus dealing with functions of numbers.

5. Graph theory method

Graph theory method in mathematical modeling is a unique method. Graph theory modeling refers to the process of abstracting and simplifying some abstract things and describing their characteristics and internal relations with graphics.