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What are the analytical methods in mathematical modeling?
Mathematical modeling is a method to abstract practical problems into mathematical models and predict and solve practical problems by solving the models. In mathematical modeling, there are many different analytical methods that can be used to solve problems. The following are some common analysis methods:

1. Mechanism analysis: This method is mainly used to describe complex objects, things and processes that are difficult to express with symbols, charts or equations. It is usually used to simulate physical phenomena.

2. Test analysis method: This method is mainly used to test whether the established model can reflect the actual problems well. Usually used for model verification and model correction.

3. Comparative analysis: This method is mainly used to compare the advantages and disadvantages of different models. Usually used for model selection.

4. Sensitivity analysis: This method is mainly used to study the influence of various parameters in the model on the results. It is usually used to optimize models.

5. Probability analysis: This method is mainly used to deal with random events and uncertain factors. It is usually used for risk assessment and decision analysis.

6. Graphical analysis: This method is mainly used to display data and results intuitively through graphical tools. It is usually used for data visualization and result interpretation.

7. Numerical analysis method: This method is mainly used to solve the equations in the model through numerical calculation. Usually used for model solving and result prediction.

8. Optimization analysis method: this method is mainly used to find the optimal solution, that is, the solution that maximizes or minimizes the objective function under certain conditions. Usually used to optimize problems.