By M. M. Woolfson

ISBN-10: 0198504233

ISBN-13: 9780198504238

ISBN-10: 019850425X

ISBN-13: 9780198504252

ISBN-10: 0585484279

ISBN-13: 9780585484273

Laptop simulation is more and more utilized in physics and engineering to foretell the possible final result of experiments and to assist of their interpretation. this article for undergraduates illustrates the elemental suggestions with various basic courses and difficulties drawn from a variety of disciplines.

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**Extra resources for An introduction to computer simulation**

**Sample text**

1 The Monte Carlo method During the Second World War scientists in the USA were working on the design of an atomic bomb and they were meeting problems which they needed to solve quickly and for the solution of which they had little previous direct experience to guide them. One such problem involved the way that neutrons would penetrate a barrier, a problem with features which made it different from, say, the absorption of light or X-rays in a medium. A neutron could react with matter in different ways - it could be unaffected, be scattered either elastically or inelastically, or be absorbed - and the probabilities of these events would be dependent on the energy of the neutron.

Xv) follows the procedure described above, with first forward and then backward substitution, to solve a set of equations with coefficients of the appropriate form. This subroutine is used with the main program HEATRI (see p. xv) to solve the temperature profile problem. 4. 10) by estimating the temperature gradient from the temperatures at i = 0 and i = 1 with the cross-sectional area at i = l/2. 131 W, is slightly different from that found from the shooting method. The diffusion equation 41 The problem we have dealt with here is a one-dimensional steady-state problem with only one independent variable which entailed the solution of a first-order ordinary differential equation.

5 for various values of At and corresponding r. 8889. 5, the value at which the explicit method became unstable, still give stable, although not necessarily accurate, results for the implicit method. The values of temperature gradually drift with increasing r but no physically unrealistic results occur until r becomes i-2 i-1 i i+1 i Fig. 7 The Crank-Nicholson equations are centred on the point (i,j+1/2) marked by a cross. The finite-difference representations involve the six terms contained in the + 2 dashed boxes.

### An introduction to computer simulation by M. M. Woolfson

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