Despite the great achievements of mathematical modeling, many real situations can not be adequately represented using appropriate mathematical models. In some cases, this is hampered by certain stiffness mathematics as a language of description and presentation of events and phenomena. In addition, even if it is possible to formalize the life situation under consideration by constructing a mathematical model, the optimization problem obtained on its basis can be too complicated for modern algorithms for solving problems of this class.
An alternative to mathematical modeling of complex systems is simulation simulation (IM) . This type of simulation is often the best (if not the only) way to study real systems.
The term imitation modeling means that we are dealing with models with which we can not calculate or predict the behavior of a system in advance, but to predict the behavior of a system, we need a computational experiment (simulation) on a mathematical The model with the given initial data [Error! The reference source was not found.].
The difference between mathematical and simulation models is that in the latter, instead of an explicit mathematical description of the relationship between input and output variables, the real system is divided into a number of sufficiently small (functionally) elements or modules. Then the behavior of the source system is simulated as the behavior of the totality of these elements, which are connected in a certain way (by establishing the appropriate interrelations between them) into a single whole. The computational implementation of such a model begins with the input element, then passes through all the elements until the output element of the model is reached.
Simulation models are usually classified according to the following most common signs:
• By the way of interaction with the user;
• how to change the model time;
• The purpose of the experiment.
The classification of simulation models is schematically shown in Fig. 3.1.
Fig. 3.1. Classification of simulation models
The simulation models can be stand-alone and interactive. The offline models do not require the researcher's intervention after determining the simulation mode and setting the initial data, user interaction with such models is reduced only to input of the initial information and to management of the beginning and the termination of work of models. Interactive models provide a dialogue with the user in a particular mode in accordance with the simulation scenario, allowing the user to suspend the simulation session/change the values of the model parameters, adjust the list of recorded data, etc.
As mentioned earlier (§1.3, Chapter 1), there are two mechanisms for modifying the model time: advancing time from event to event and advancing time with a constant step.
The process of constructing simulation models is the sequential execution of simulation steps. Stages of simulation modeling, as well as of any other type of modeling, are summarized and presented in § 1.3. Ch. 1 of this tutorial.
The above-mentioned stages of imitation research are rarely performed in a strictly defined sequence, from the definition of the problem to the documentation. In the course of the simulation, there may be malfunctions in the model runs, erroneous assumptions, which subsequently have to be abandoned, that is, at each stage it is possible to return back to the previous stages. It is this iterative process that will enable us to obtain a model that allows us to make decisions.
The computational aspects of simulation models are usually relatively simple, but, as a rule, very laborious. Therefore, the implementation of such models implies the use of computer technology.
Simulation models are much more flexible in representing real systems than their mathematical "competitors". The reason for this flexibility lies in the fact that in simulation modeling the initial system is considered at an elementary level, while mathematical models tend to describe systems at a global, as much as possible general level.
But for the flexibility of simulation models have to pay high requirements for consumed time and computing resources. Therefore, the implementation of some simulation models, even on modern fast and high-performance computers can be very slow.
Thus, simulation modeling is a powerful tool for investigating the behavior of real systems. Methods of simulation allow you to collect the necessary information about the behavior of the system by creating its computerized model. This information is then used to design the system. The main advantage of the IM:
• the ability to describe the behavior of components (elements) of processes or systems at a high level of detail;
• no limitations between the parameters of the MI and the state of the external environment;
• the possibility of studying the dynamics of interaction of components in time and space of the system parameters .
These advantages provide the imitating method of wide dissemination.
It is recommended to use simulation simulation in the following cases:
1. If there is no complete formulation of the research task and the process of cognition of the modeling object is in progress. The simulation model serves as a means of studying the phenomenon.
2. If analytical methods are available, but mathematical processes are complex and time-consuming, simulation simulation provides a simpler way to solve the problem.
3. When, in addition to assessing the impact of the parameters (variables) of the process or system, it is desirable to monitor the behavior of the components (elements) of the process or system during a certain period.
4. When simulation is the only way to study a complex system because of the impossibility of observing phenomena under real conditions (reactions of thermonuclear fusion, space exploration).
5. When it is necessary to control the flow of processes or the behavior of systems by slowing or accelerating phenomena during simulation.
6. When training specialists for new technology, when simulations provide the opportunity to acquire skills in the operation of new technology.
7. When new situations in the behavior of real processes and systems are studied. In this case, the simulation serves to test new strategies and rules for conducting full-scale experiments.
8. When the sequence of events in the projected processes and systems is of particular importance, and the model is used to predict the bottlenecks in their functioning. 
However, along with advantages, MI has drawbacks:
• The development of a good MI is often more expensive than creating an analytical model and requires a lot of time;
• It may be that the IM is inaccurate (which is often the case), and the researcher is not able to measure the degree of this inaccuracy;
• Often researchers turn to MI without presenting those difficulties with which they will meet, and make a number of methodological mistakes .
And yet, MI is one of the most widely used methods for solving problems of synthesis and analysis of complex processes and systems.
Also We Can Offer!
- Argumentative essay
- Best college essays
- Buy custom essays online
- Buy essay online
- Cheap essay
- Cheap essay writing service
- Cheap writing service
- College essay
- College essay introduction
- College essay writing service
- Compare and contrast essay
- Custom essay
- Custom essay writing service
- Custom essays writing services
- Death penalty essay
- Do my essay
- Essay about love
- Essay about yourself
- Essay help
- Essay writing help
- Essay writing service reviews
- Essays online
- Fast food essay
- George orwell essays
- Human rights essay
- Narrative essay
- Pay to write essay
- Personal essay for college
- Personal narrative essay
- Persuasive writing
- Write my essay
- Write my essay for me cheap
- Writing a scholarship essay