First, understand the problem.
Before mathematical modeling, it is necessary to have a deep understanding of the problem. It is necessary to clarify the actual background, objectives and constraints of the problem. This includes abstracting and simplifying problems, and transforming practical problems into mathematical models.
Second, establish a mathematical model.
On the basis of understanding the problem, we need to use mathematical language and tools to build the model. This process includes defining variables, establishing equations or inequalities, and determining model parameters. According to the characteristics and needs of practical problems, the mathematical model can be linear, nonlinear, continuous or discrete.
Third, solve the mathematical model.
Once the mathematical model is established, it needs to be solved. This may involve numerical calculation, symbolic operation, optimization and other methods. The solution of mathematical models usually requires the use of computers and related mathematical software, such as MATLAB and Python.
Fourth, verify and modify the model.
After the model is solved, it is necessary to compare the results with the actual data to verify the accuracy and effectiveness of the model. If the results of the model are quite different from the actual data, the model needs to be revised and improved. This may involve adjusting the parameters of the model or reconstructing the structure of the model.
Understanding problems and building models
1, understand the actual background and objectives of the problem.
Before modeling, it is very important to deeply understand the actual background and objectives of the problem. This includes abstracting and simplifying problems, and transforming practical problems into mathematical models. In order to better understand the problem, it may be necessary to collect relevant data and information, and communicate and discuss with relevant personnel.
2. Define variables and establish equations.
After understanding the problem, we need to use mathematical language and tools to build the model. This includes defining variables, establishing equations or inequalities, and determining model parameters. The choice of variables needs to consider the actual needs of the problem and the availability of data, and the establishment of equations needs to consider the physical laws and mathematical principles of the problem.