کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6421189 | 1631820 | 2014 | 17 صفحه PDF | دانلود رایگان |

For the generalized Fermi-Dirac integrals, Fk(η,β), of orders k = â1/2, 1/2, 3/2, and 5/2, we explicitly obtained the first 11 terms of their Sommerfeld expansions. The main terms of the last three orders are rewritten so as to avoid the cancelation problem. If η is not so small, say not less than 13.5, 12.0, 10.9, and 9.9 when k = â1/2, 1/2, 3/2, and 5/2, respectively, the first 8 terms of the expansion assure the single precision accuracy for arbitrary value of β. Similarly, the 15-digits accuracy is achieved by the 11 terms expansion if η is greater than 36.8, 31.6, 30.7, and 26.6 when k = â1/2, 1/2, 3/2, and 5/2, respectively. Since the truncated expansions are analytically given in a closed form, their computational time is sufficiently small, say at most 4.9 and 6.7 times that of the integrand evaluation for the 8- and 11-terms expansions, respectively. When η is larger than a certain threshold value as indicated, these appropriately-truncated Sommerfeld expansions provide a factor of 10-80 acceleration of the computation of the generalized Fermi-Dirac integrals when compared with the direct numerical quadrature.
Journal: Applied Mathematics and Computation - Volume 234, 15 May 2014, Pages 417-433