On the Highly Accurate Evaluation of the Voigt/Complex Error Function with Small Imaginary Argument

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 ≤ 0.1. Error analysis and run-time tests in double-precision arithmetic reveals that in the real and imaginary parts, the proposed algorithm provides an average accuracy exceeding 10−15 and 10−16, respectively, and the calculation speed is as fast as that reported in recent publications. An optimized MATLAB code providing rapid computation with high accuracy is presented.