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

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 $0\le y<0.1\cap \mid x+iy\mid \le 8$. A Matlab code for computation of the complex error function with entire coverage of the complex plane is presented.