On the very accurate evaluation of the Voigt/complex error function with small imaginary argument

TL;DR

This paper introduces a rapidly convergent series for highly accurate evaluation of the Voigt/complex error function with small imaginary parts, achieving near machine precision and fast computation in double-precision environments.

Contribution

It presents a new series expansion method for the Voigt function that offers superior accuracy and efficiency for small imaginary arguments compared to existing algorithms.

Findings

Accuracy exceeds 10^-15 in real parts and 10^-16 in imaginary parts.

The proposed algorithm is as fast as recent methods.

An optimized MATLAB implementation is provided.

Abstract

A rapidly convergent series, based on Taylor expansion of the imaginary part of the complex error function, is presented for highly accurate approximation of the Voigt/complex error function with small imaginary argument (Y less than 0.1). Error analysis and run-time tests in double-precision computing platform reveals that in the real and imaginary parts the proposed algorithm provides average accuracy exceeding 10^-15 and 10^-16, respectively, and the calculation speed is as fast as that of reported in recent publications. An optimized MATLAB code providing rapid computation with high accuracy is presented.