Master-Slave Algorithm for Highly Accurate and Rapid Computation of the Voigt/Complex Error Function

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Date

2014-06

Authors

Abrarov, S. M.
Quine, B. M.

Journal Title

Journal ISSN

Volume Title

Publisher

Journal of Mathematics Research

Abstract

We obtain a rational approximation of the Voigt/complex error function by Fourier expansion of the exponential function e(t−2σ)2 and present master-slave algorithm for its efficient computation. The error analysis shows that at y>10−5 the computed values match with highly accurate references up to the last decimal digits. The common problem that occurs at y→0 is effectively resolved by main and supplementary approximations running computation flow in a master-slave mode. Since the proposed approximation is rational function, it can be implemented in a rapid algorithm.

Description

Keywords

complex error function, complex probability function, Voigt function, Faddeeva function, plasma dispersion function, complementary error function, error function, Fresnel integral, Dawson’s integral, master-slave algorithm

Citation

S. M. Abrarov and B. M. Quine, “Master-Slave Algorithm for Highly Accurate and Rapid Computation of the Voigt/Complex Error Function,” Journal of Mathematics Research, vol. 6, no. 2, May 2014.