If mathematical regularities of the course of any given process are known, and process is dangerous or its implementation demands considerable expenses, it is possible to carry out its modeling. It can be carried out on paper, by means of computer facilities, or through other, less dangerous or expensive process submitting to the same regularities.
Instruction
1. To carry out mathematical modeling of process on paper, first of all, find in textbooks or reference books of a formula, the regularities characterizing it. In advance set up in all formulas those from parameters which are constants. Now find unknown information on the process course in any given its stage, having substituted in a formula the known data on its course in this stage. For example, it is necessary to model change of the power which is allocated on the resistor depending on tension at it. In this case, it is necessary to use the known combination of formulas: I=U/R, P=UI
2. If necessary, make the schedule or family of schedules about all course of process. For this purpose break its course into a number of points (the their more, the more precisely result, but longer than calculation). Carry out calculations for each of points. Calculation will be especially labor-consuming in case several parameters as it is necessary to carry out it for all of them combinations independently of each other change.
3. If the volume of calculations is considerable, use computer facilities. Use that programming language which you well own. In particular, to calculate change of power on loading with a resistance of 100 Ohms at change of voltage from 1000 to 10000 V with a step to 1000 V (in reality it is difficult to construct such loading as the maximum power on it will reach megawatt), it is possible to write such program in the BASIC language: 10 R=10020 FOR U=1000 TO 10000 STEP 100030 I=U/R40 P=U*I50 PRINT U,I,P60 NEXT U70 END
4. If desired, use for modeling of one process to another, submitting same regularities. For example, the mathematical pendulum can be replaced with an electric oscillatory contour, or on the contrary. Sometimes there is an opportunity to use as modeling the same phenomenon, as modelled, but in the reduced or increased scale. For example, if to take already mentioned resistance in 100 Ohms, but to give on it tension in the range not from 1000 to 10000, but from 1 to 10 V, then the power allocated on it will change not from 10000 to 1000000 W, but from 0.01 to 1 W. Such installation will go in on a table, and the allocated power can be measured by a usual calorimeter. After that the result of measurement will need to be increased by 1000000. Consider that not all phenomena give in to scaling. For example, it is known that if all details of the heat engine to reduce or increase in identical number of times, that is, in proportion, then probability is high that it will not start working. Therefore at production of engines of the different sizes the coefficients of increase or reduction for each of its details take various.