The evaluation of the Arrhenius integral with special reference to small computers

This paper discusses the factors which influence the choice and implementation of computer methods to evaluate the Arrhenius integral, I_A = ∫^Tα₀ exp(?E/RT)dT. It also identifies the sources of computational error and inefficiency. It is shown that, amongst numerical integration techniques, the classical trapezoidal and Simpson rules have little to recommend them compared with the method of Gaussian quadrature. A technique for preserving the accuracy of the Gauss method at very high values of E/RT_α is also described and evaluated. Rational (Padé) approximation is found to compare favourably with Gaussian quadrature in efficiency and accuracy, and is simpler to use. The discussion also reveals that six decimal-digit arithmetic is adequate for all practical purposes.