The Seven Steps of Mathematical Modeling, the General Steps of Mathematical Modeling

Restatement of the problem. I think this is very simple, don't think too hard, this is to repeat the problem to be solved, of course, as much as possible.

Assumptions of the model. It is to make assumptions about the existing problems after analyzing the problem, and then you can use your rich imagination to assume what so-and-so will be.

Definition of symbols. Explain the individual symbols of your formula.

Establishment of the model.

Building a functional model is a relatively flexible problem, and there is no definite method to follow, and only by doing more exercises can you gradually master it. Use your powerful imagination to connect your theoretical knowledge and build models. Draw relevant diagrams. Remember to check all kinds of relevant information and literature.

Solving the model. Solving this requires your logical skills. It doesn't matter if you don't understand, the key is that you have to be able to learn, and you can find a way to solve any equation you don't understand on the Internet.

It's important to learn and use now. Even those who have learned will forget, so your ability to learn quickly determines your future direction, and this is my opinion.

The main steps of mathematical modeling.

The main steps of mathematical modeling.

First, model preparation.

First of all, it is necessary to understand the actual background of the problem, clarify the purpose of modeling, collect all kinds of necessary information, and try to understand the characteristics of the object.

Second, model assumptions.

According to the characteristics of the object and the purpose of modeling, the necessary and reasonable simplification of the problem, and the assumption in precise language are made.

mold is a crucial step. If all the factors of the problem are taken into account, it is undoubtedly an act of courage but poor method, so.

Skilled modelers are able to give full play to their imagination, insight and judgment, and are good at distinguishing between priorities and priorities, and in order to make the process simple, they should be.

Try to make the problem linearized and homogeneous.

The general steps of mathematical modeling are as follows:

1. Practical problems are abstracted, simplified, and assumed to determine variables and parameters.

2. Establish a mathematical model and solve and determine the parameters mathematically and numerically.

3. Test the mathematical model with the measured data of the actual problem.

4. Conform to the actual situation and deliver the use, so as to produce economic and social benefits; Not realistic, remodeled.

Classification of mathematical models:

1. According to the research method and the mathematical characteristics of the object, it is divided into: elementary model, geometric model, optimization model, differential equation model, graph theory model, logical model, stability model, statistical model, etc.

2. According to the actual field (or discipline) of the research object, it is divided into: population model, transportation model, environmental model, ecological model, physiological model, urban planning model, water resources model, pollution model, economic model, social model, etc.

Mathematical modeling. The order of the five steps is as follows:

The first step is to determine what kind of natural things or natural phenomena the research object belongs to according to the characteristics of the research object, so as to determine what kind of mathematical method to use and what kind of mathematical model to establish.

That is, first determine whether the object belongs to the "necessary" class or the "random" class of the mathematical model that should be used. Is it a "mutant" class, or a "fuzzy" class.

Step 2: Identify several basic quantities and basic scientific concepts to reflect the state of the object of study. This needs to be determined based on the analysis of existing scientific theories or hypotheses and experimental information. For example, in the study of mechanical systems, the facsimile physical quantities are first determined.

It is the mass principal (m), velocity (v), and acceleration.

, time (t), vector (r), etc.

It is necessary to pay attention to the fact that there are not too many fundamental quantities to be determined, otherwise there are too many unknowns, and it is difficult to simplify them into possible mathematical models, so it is necessary to select substantial and critical physical quantities.

Step 3: Grasp the main contradiction for scientific abstraction. The object of actual research is complex, and many factors are mixed together, so it is necessary to change the complex object of study into a simple and idealized object of study, and it is quite difficult to achieve this, and the key is to distinguish priorities.

How to distinguish priorities can only be analyzed on a case-by-case basis.

However, there are also two basic principles: first, the mathematical model must be possible, at least an approximate solution; Second, the error of the approximate solution cannot exceed the allowable error range of the actual problem.

Step 4: Calibrate the simplified basic quantities and give their scientific connotations. That is, to indicate which are constants.

Which are known, which are to be sought, which are vectors, and which are scalars.

What is the physical meaning of these quantities?

Step 5: Find the result according to the mathematical model.

Mathematical modeling is the method of solving various practical problems by building mathematical models. There is no fixed format and standard for mathematical modeling, and there is no clear method, there are usually 6 steps: 1. Clarify the problem; 2. Reasonable assumptions; 3. Build a model; 4. Solve the model; 5. Analysis and inspection;

6. Model interpretation. Mathematical modelling deals with practical problems in various fields, which are often vague and difficult to find the key point directly, and cannot clearly state what methods should be used. Therefore, the first task of building a model is to identify the problem.