First, model preparation.
First of all, we should understand the actual background of the problem, clarify the modeling purpose, collect all kinds of necessary information, and try our best to understand the characteristics of the object.
Second, the model hypothesis.
According to the characteristics of the object and the purpose of modeling, it is necessary and reasonable to simplify and assume the problem with accurate language.
A key step in the model. If we consider all the factors of the problem, this is undoubtedly a brave but clumsy method, so
Excellent modelers can give full play to their imagination, insight and judgment, and are good at distinguishing priorities. Furthermore, in order to simplify the processing methods, they should
Try to linearize and homogenize the problem.
Third, the model composition.
According to the assumptions made, the causal relationship of the object is analyzed, and various quantities are constructed by using the internal laws of the object and appropriate mathematical tools.
Equation relations or other mathematical structures. At this time, we will enter the vast world of applied mathematics, where high numbers and old probabilities are used.
There are many lovely children under people's knees, such as graph theory, queuing theory, linear programming, game theory and so on. It's really great.
Big country, there is a hole in the sky. But we should remember that the purpose of establishing mathematical model is to make more people understand and apply it, so it is necessary to establish mathematical model.
The simpler, the more valuable.
Fourth, the model is solved.
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 operations and so on. The solution of a practical problem often needs complicated calculation, and in many cases, the operation of the system needs calculation.
Computer simulation, so programming ability and familiarity with mathematical software packages are very important.
Fifth, model analysis.
Mathematically analyze the model solution. "Cross as a ridge side into a peak, far and near? Quot, can you make a model result?
Careful and accurate analysis determines whether your model can reach a higher level. Also remember, in either case, you need to make mistakes.
Analysis and data stability analysis.
The main methods used in mathematical modeling are:
(1) Mechanism analysis method: Based on the understanding of the characteristics of objective things, the model is derived from the basic physical laws and the structural data of the system.
Type.
1, proportional analysis: the most basic and commonly used method to establish the functional relationship between variables.
2. Algebraic method: the main method to solve discrete problems (discrete data, symbols, graphics).
3. Logical method: it is an important method in the study of mathematical theory, and it is of great significance to the practical problems in sociology and economics in decision-making and countermeasures.
It has been widely used in other disciplines.
4. Ordinary differential equation: The key to solving the change law between two variables is to establish the expression of "instantaneous change rate".
5. Partial differential equation: solving the change law between the dependent variable and more than two independent variables.
(2) Data analysis method: Through the statistical analysis of the measured data, find out the model that best conforms to the data.
1. regression analysis method: the function expression of a set of observed values (xi, fi) i = 1, 2, n used to determine the function f(x) is determined by the following formula.
It deals with static independent data, so it is called mathematical statistics method.
2. Time series analysis: dealing with dynamic related data, also known as process statistics.
3. Regression analysis method: the expression i = 1, 2, n of the function f(x) used to determine a group of observed values (xi, fi) is determined by the following formula.
It deals with static independent data, so it is called mathematical statistics method.
4. Time series analysis: dealing with dynamic related data, also known as process statistics.
(3), simulation and other methods
1. simulation: It is essentially a statistical estimation method, which is equivalent to sampling inspection. (1) discrete system simulation, with one set.
State variables. ② Continuous system simulation, with analytical expression or system structure diagram.
2. Factor test method: the system is tested locally, and then the required model structure is obtained through continuous analysis and modification according to the test results.
3. Artificial reality method: Based on the understanding of the past behavior and future goals of the system, and taking into account the related factors of the system.
May change, artificially form a system.