| Summary: | 碩士 === 國立臺灣海洋大學 === 資訊工程學系 === 98 === This paper mainly investigates numerical methods for evaluating the
Fermi-Dirac function. The Fermi-Dirac function, which arises from semi-
conductor physics and astrophysics, is defined by
F_{j}(x)=\frac{1}{\Gamma(1+j)}\int_{0}^{\infty}\frac{t^j}{e^{t-x}+1}\,dt , −∞ < x < ∞ ,
where j is integer or half of integer bearing a particular meaning in
physics.
Since the class of functions involves an integral over infinite range,
there is no corresponding function (closed form) to this improper integral
except for some integers of j. In general, it is difficult to find the exact
value, we therefore have to rely on numerical methods to approximate
the values of the class of functions.
Over several decades, many numerical methods were proposed, how-
ever, the accuracy and efficiency of the existing schemes are quite re-
stricted. According to our experiments, our new approach can perform
highly accurately and efficiently, provided a suitable choice of parame-
ters, M (positive constant), h (step size), and N (the number of function
evaluations). We also compared our method with the popular schemes,
such as Goano’s algorithm, Lether’s method, and the lastest approach
of Mohankumar. It is evident that our scheme works quite well and
competitively.
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