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

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.

37 pages, 7 figures

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