On the Adaptive Quadrature of Fermi-Dirac Functions and their Derivatives

Abstract

In this paper, using the Python SciPy module “quad”, a fast auto-adaptive quadrature solver based on the pre-compiled QUADPACK Fortran package, computational research is undertaken to accurately integrate the generalised Fermi-Dirac function and all its partial derivatives up to the third order. The numerical results obtained with quad method when combined with optimised break points achieve an excellent accuracy comparable to that obtained by other publications using fixed-order quadratures.