A rational approximation of the Dawson's integral for efficient computation of the complex error function

TL;DR

This paper introduces a rational approximation method for Dawson's integral that enables high-accuracy and rapid computation of the complex error function across a broad domain, with a provided Matlab implementation.

Contribution

The authors present a novel rational approximation of Dawson's integral that achieves high precision and efficiency for computing the complex error function.

Findings

Accuracy exceeding 10^-14 in the specified domain

Rapid computation suitable for practical applications

Complete Matlab code implementation provided

Abstract

In this work we show a rational approximation of the Dawson's integral that can be implemented for high-accuracy computation of the complex error function in a rapid algorithm. Specifically, this approach provides accuracy exceeding $\sim {10^{ - 14}}$ in the domain of practical importance $0 \le y < 0.1 \cap \left| {x + iy} \right| \le 8$. A Matlab code for computation of the complex error function with entire coverage of the complex plane is presented.