Common ideas and methods in mathematical modeling: analogy, dichotomy, dimensional analysis, difference method, variational method, graph theory, analytic hierarchy process, data fitting method, regression analysis method, mathematical programming, mechanism analysis method, queuing theory, countermeasure method, decision method, fuzzy evaluation method, time series method, grey theory method and modern optimization algorithm.
Model preparation
Understand the actual background of the problem, clarify its practical significance, and master all kinds of information of the object. The essence of the problem is contained in mathematical thought and runs through the whole process of the problem, and then the problem is described in mathematical language. Requirements in line with mathematical theory, in line with mathematical habits, clear and accurate.
According to the characteristics of the actual object and the purpose of modeling, the problem is simplified with accurate language and some appropriate assumptions are put forward. On the basis of assumptions, use appropriate mathematical tools to describe the mathematical relationship between variables and constants, and establish the corresponding mathematical structure (try to use simple mathematical tools).