A handy, accurate, invertible and integrable expression for Dawson’s function

Abstract

This article proposes a handy, accurate, invertible and integrable expression for Dawson’s function. It can be observed that the biggest relative error committed, employing the proposed approximation here, is about 2.5%. Therefore, it is noted that this integral approximation to Dawson’s function, expressed only in terms of elementary functions, has a maximum absolute error of just 7 × 10^-3. As a case study, the integral approximation proposed here will be applied to a nonclassical heat conduction problem, contributing to obtain a handy, accurate, analytical approximate solution for that problem