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 $0 \le y < 0.1 \cap \left| {x + iy} \right| \le 8$. A Matlab code for computation of the complex error function with entire coverage of the complex plane is presented. 
S. M. Abrarov and B. M. Quine
math.NA