By M. M. Woolfson
Desktop simulation is more and more utilized in physics and engineering to foretell the possible consequence of experiments and to assist of their interpretation. this article for undergraduates illustrates the fundamental concepts with a variety of basic courses and difficulties drawn from quite a lot of disciplines.
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Extra info for An introduction to computer simulation
Consider the continuous function y = f ( x ) shown in Fig. 1 and assume that the value at x = X, f(X), is known together with the values of all the derivatives at that point. To estimate the value at some other point, x = X+h, we can use the Taylor series The remainder, Rn+1 , represents the error when the series is truncated after n + 1 terms and, as long as the function is differentiable up to f ( n + l ) , it can Fig. 1 The curve y=f(x). 34 Finite-difference methods always be expressed in the form where £ is in the range X to X + h.
10, where the satellite is shown approaching the near point. It is stretched by the tidal force, but due to inertia the satellite tidal bulge lags behind the radius vector. The departure of the satellite from a spherical form can be thought of as a sphere plus two bobs of matter at the points P and Q and the gravitational forces on these are shown. Since the force at P will be greater than that at Q there will be a net torque imparting angular momentum to the satellite, causing it to spin faster.
The above just gives the flavour of the range of particle methods and their applications. A full treatment, with detailed descriptions of the methods and examples of their use, will be given in Chapters 3 and 7. 3 Continuum physics - the finite-difference method There are many problems in physics where some property of a material temperature, density or solvent concentration, for example - varies continuously in space and time and where the rates of change from point to point are described by partial differential equations.
An introduction to computer simulation by M. M. Woolfson