Basic Concepts in Computational Physics by Benjamin A. Stickler & Ewald Schachinger

Author:Benjamin A. Stickler & Ewald Schachinger
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

result after N = 103 experiments for both generators.

14.2 Monte-Carlo Integration

We generalize the ideas formulated above and consider a function f(x) ≥ 0 for where the area of interest is

(14.4)

We denote

(14.5)

and obtain using the above example

(14.6)

where n is the number of random points under the curve indicated schematically in Fig. 14.2. The area A s is given by

(14.7)

and the random numbers r i  = (x i , y i ) are uniformly distributed within the intervals x i  ∈ [a, b] and . This method is referred to as hit and miss integration [4].

Fig. 14.2Schematic illustration of the Monte-Carlo integration technique

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.