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Astron. Astrophys. 331, 1103-1107 (1998)

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4. Comparison with numerical results

Figs. 1a and 1b show how the theoretical results for [FORMULA] all agree with the numerical simulation based on the method of MC. 10,000 realizations were used with 10,000 steps in x. For both [FORMULA] and [FORMULA] the agreement is so good that the theoretical and numerical curves can hardly be distinguished. The very slight differences arise for two reasons. Firstly, because of the finite number of realisations there is a small residual noise component present. Secondly, there is a cumulative error in the numerical integration because of the finite step size in x.


[FIGURE] Fig. 1a and b. a [FORMULA] and b   [FORMULA] are plotted for [FORMULA]. In both graphs, the upper curve is for [FORMULA], the middle curve is for [FORMULA] and the lower curve is for [FORMULA] (for [FORMULA], [FORMULA] is just zero).

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© European Southern Observatory (ESO) 1998

Online publication: March 3, 1998
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