ARTICLE | doi:10.20944/preprints202302.0082.v1
Subject: Computer Science And Mathematics, Applied Mathematics Keywords: arctangent function; midpoint integration; iterative algorithm; constant pi
Online: 6 February 2023 (07:11:07 CET)
In this work we derive a generalized series expansion of the acrtangent function by using the enhanced midpoint integration (EMI). Algorithmic implementation of the generalized series expansion utilizes a simple two-step iteration. This approach significantly improves the convergence and requires no surd numbers in computation of the arctangent function.
ARTICLE | doi:10.20944/preprints202208.0404.v1
Subject: Computer Science And Mathematics, Applied Mathematics Keywords: complex error function; Faddeeva function; Voigt function; interpolation
Online: 24 August 2022 (03:31:12 CEST)
In this work we develop a new algorithm for efficient computation of the Voigt/complex error function. In particular, in this approach we propose a two-domain scheme where number of the grid-points is dependent on the input parameter $y$. The error analysis we performed shows that the MATLAB implementation meets the requirements for radiative transfer applications involving the HITRAN spectroscopic database. The run-time test shows that this MATLAB implementation provides rapid computation especially at smaller range of the parameter x.