From the middle of the last century in various areas of human activity began to enter computers and mathematical methods.They began to appear new disciplines such as mathematical economics, mathematical linguistics, mathematical chemistry, and others, which were the subject of study mathematical models of phenomena and objects, as well as methods of their study.
mathematical model - is an approximate description of the mathematical language of objects or phenomena of the real world.The main objective of the simulation performs research data objects and predict the results of future observations.In addition, modeling is a method of knowledge and the environment, the world, which allows you to control.
Using mathematical modeling is indispensable in cases where for various reasons difficult or impossible to produce a natural experiment.For example, it is difficult to check whether it is true or that cosmological theory, or study the effects of a nuclear explosion.But all of this can be seen on the computer, pre-constructing a mathematical model.
Mathematical model: design stages
Firstly, the construction of a model is made.To do this, consider a natural phenomenon, an economic plan, design, production process or other non-mathematical object.First, define the features of the phenomena and their relationships at a qualitative level.Next obtained depending on the form is converted into a formula or mathematical model.This step is the most difficult.
The second step is performed for solving mathematical problems formulated on the basis of the model.It focuses on a development of numerical methods and algorithms for solving the problem on a computer that allow for the time allowed to receive the result with the required accuracy.
The next step is the interpretation of the consequences arising from the model, translating the results of a mathematical language in the form adopted in the study area.
then checked the adequacy of the resulting model, find out whether the results of the investigation within the specified accuracy.
At the final stage modification of the model.It is difficult for most or adequacy of validity or make it easier to reach an acceptable practical solution.
Classification of mathematical models
There are different criteria for the division of mathematical models in the group.So, by the nature of problems to be solved to make the division of the structural and functional models.At the same time describing the object or phenomenon values are expressed quantitatively.
structural mathematical model presented in the form of different types of equations (algebraic, differential), which establish between the studied variables quantitative dependence.In this regard as variables as independent variables, and functions derived from these.
Functional models describe complex objects consisting of several separate elements, between which some connections.Typically, the data communication is difficult or impossible to quantify.For their study using graph theory, mathematical objects that represent the set of points in space or on a plane.
By the nature of forecasting results and the original data model is divided into static probabilistic and deterministic.The first type is based on the collected statistics, and produced by them forecasts are probabilistic.
Examples of mathematical models can be attributed to the problem of the flight of the projectile, transport and other tasks.