Changing the original requirements and re-modeling can be done here.

Don't play with new mathematical terms when popularizing or improving the direction.

Mathematically analyze the model solution. "From the other side of the mountain, the distance is different." Whether you can analyze the model results carefully and accurately determines whether your model can reach a higher level. Also remember that in either case, error analysis and data stability analysis are needed.

Some models (such as nonlinear differential equations) need stability or other qualitative analysis. At this time, it is necessary to point out the mathematical theory on which it is based and draw a clear conclusion on the basis of reasoning or calculation.

In the process of model establishment and analysis, conclusions with universal significance can be expressed in the form of clear theorems or propositions. Conclusion the problems that should be paid attention to in use can be listed in the form of mnemonics. Theorems and propositions must clearly state the conditions for the conclusion to be established.

This mathematical model can be discussed from many aspects. For example, we can explore how the model will change for different scenarios. Or according to the actual situation, we can change some assumptions made at the beginning of the article and point out the changes in the mathematical model. Different numerical methods can also be used to calculate and compare the results. Sometimes we should broaden our thinking and consider the changes brought about by different modeling methods.