A simple reform for treating the loss of accuracy of Humlicek's W4 algorithm near the real axis

TL;DR

This paper introduces a straightforward modification to Humlicek's W4 algorithm to improve its accuracy near the real axis when calculating the Faddeyeva function, ensuring reliable results across a broad domain.

Contribution

The authors propose a simple reformulation of Humlicek's W4 algorithm that preserves its accuracy near the real axis for the Faddeyeva function calculations.

Findings

Maintains accuracy over a wide domain of the real part x

Effective for y in the range [10-30, 10+30]

Simple implementation without significant computational overhead

Abstract

We present a simple reform for treating the reported problem of loss-of-accuracy near the real axis of Humlicek's w4 algorithm, widely used for the calculation of the Faddeyeva or complex probability function. The reformed routine maintains the claimed accuracy of the algorithm over a wide and fine grid that covers all the domain of the real part, x, of the complex input variable, z=x+iy, and values for the imaginary part in the range y=[10-30, 10+30]