By M. M. Woolfson
Laptop simulation is more and more utilized in physics and engineering to foretell the possible final result of experiments and to help of their interpretation. this article for undergraduates illustrates the elemental recommendations with a number of uncomplicated courses and difficulties drawn from quite a lot of disciplines.
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Extra info for An introduction to computer simulation
2. This estimate is a forward-difference estimate since it gives the slope at x = X from the value of f (X) and the value at one increment of x in the forward direction, that is, f(X+h). 1 Taylor series estimates with four terms included. 015854 Ordinary derivatives 35 Fig. 2 Estimates of f'(x) from: forward difference (slope of chord BC); backward difference (slope of chord AB); and central difference (slope of chord AC). 4) is the dominant one. This can be written as The error is indicated as +O(h), but that is not to say that the error is necessarily positive.
2 The use of finite differences Consider the following problem, illustrated in Fig. 3. A bar of length 1 m has a circular cross-section, the radius of which varies linearly from 2cm at one end to 1 cm at the other. The curved sides of the bar are heavily lagged and the wide end and narrow end are constrained to be at temperatures 500 K and 300 K respectively. The thermal conductivity of the material of the bar is 200 W m - 1 K - 1 . Find the rate of heat flow along the bar and also determine the temperature at intervals of 10cm along its length.
If the system under investigation is a system of planets orbiting the Sun, then the number of bodies is small, the force law governing their motions is well known and the only limitation in the accuracy of the simulation is the amount of computational effort that is brought to bear. On the other hand, the physics of the system we are examining might be quite well known but the system may be so large and complex - a galaxy of 1011 stars, for example - that we cannot hope to simulate it perfectly.
An introduction to computer simulation by M. M. Woolfson