H. AMAMOU ET AL. 727
0
244:0.1:248 nm,246 nm,
0.3 nm,0.3 nm
DL
thus the parameter .
0.8326a
Our formula is also a very interesting method for easy
calculation of the Voigt function. For the calculation of
the integrals of Equation (2) the trapezoidal rule method
and the adaptive Simpson’s method give very good re-
sults.
Table A1 (Appendix 2) gives the values of the Voigt
function calculated with the Formula (2) for the very
small values of the parameter a where the calculation is
notoriously difficult [12]. This table gives also the com-
putation time(s) for the values of each column of the
table. This calculation time depends obviously on the
performances of the computer. The computer that we
have used has a processor Intel pentium 2.3 GHz and a
memory (RAM) 4 GHz. This table gives the reference
values of the Voigt function calculated from Equation
(2).
Table 1 gives a comparison between our results of
calculation of Voigt function in the in the region of very
small values of the parameter a with those of the various
algorithms of other authors.
3. Conclusion
The new representation integral for Voigt function that
we have demonstrated and used to adjustment “fitting”
of lines spectral in a precedent article is used in this work
for calculation of Voigt function. Thus, this function is
easily calculable. We also made a comparison between
the results obtained by our formula and those obtained by
the various algorithms of other authors in the region of
Table 1. Comparison between our results and the results of
various algorithms of other authors (D is here for 10).
Calculation of Voigt in the region
of very small values of the parameter a
Author u = 5.4 a = 10−10 u = 5.5a = 10−14
Amstrong et al. [13] 12
2.260842D 14
7.307387Da
Humliek [14] 12
2.260842D 16
1.966215Da
Humliek [15] 12
2.260845D 14
7.307387Da
Hui [16] 8
2.667847
9
9.238980Da
Lether and Wenston [17] 12
2.260845D 14
7.307386Da
Mclean et al. [18] 5
4.89872D
5
4.24886Da
Poppe and Wiyers [19] 12
2.260850D 14
7.307805Da
Shippony and Read [1] 12
2.260845D 14
14
7.287724Da
Zaghloul [8] 12
2.260844D 7.287724Da
This Works 12
2.260844D 14
7.307387Da
very small values of the parameter a where the calcula-
tion is notoriously difficult.
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