How to establish the mathematical model of Xiaolangdi dispatching
Generally speaking, the establishment of mathematical model can be divided into several stages: expression, solution, explanation and verification. Through these stages, the real object is transformed into a mathematical model, and then the mathematical model is returned to the real object. There is no fixed model for establishing mathematical model.
Classification of mathematical models
There are different points based on different starting points:
According to the application fields of the model, it is divided into population model, traffic model, environment model, ecological model, urban planning model, water resource model, renewable resource utilization model, pollution model and so on. If the category is larger, it will form many marginal disciplines such as biological mathematics, medical mathematics, geological mathematics, quantitative economics, mathematical sociology and so on.
According to the method of establishing the model, it can be divided into initial mathematical model, geometric model, differential equation model, graph theory model and so on.
The function of mathematical model
Mathematics is a science that studies quantitative relations and spatial forms in the real world. Its appearance and many major developments are closely related to the production activities in the real world and the needs of other corresponding disciplines. Generally speaking, when practical problems require us to provide quantitative analysis, prediction, decision-making and control results. It is often inseparable from the application of mathematics, and the establishment of mathematical model is the key link in this process.
Analysis is usually a quantitative study of a phenomenon of a real object or a quantitative description of a feature. For example, study the competition and interdependence between different groups of organisms living in the same natural environment; To describe the changing law of drug concentration in human body in order to analyze the curative effect of drugs.
Prediction is generally based on the inherent characteristics of the object to predict the development law of the object when time or environment changes. Population forecast, weather forecast and the forecast of infectious disease climax can all be used as examples.
Decision-making has a wide range of meanings, such as making a decision to optimize a quantitative index according to the law of object satisfaction. The price strategy of maximizing economic benefits and the equipment maintenance scheme of minimizing total cost are all such decisions.
Control generally refers to giving a satisfactory control scheme as far as possible according to the characteristics of the object and some indicators. For example, the control of temperature and flow in chemical production process, the control of communication by traffic lights, etc.