Abstract
A rapidly convergent series, based on Taylor expansion of the imaginary part of the complex error function, is presented for highly accurate approximation of the Voigt/complex error function with small imaginary argument y ≤ 0.1. Error analysis and run-time tests in double-precision arithmetic reveals that in the real and imaginary parts, the proposed algorithm provides an average accuracy exceeding 10−15 and 10−16, respectively, and the calculation speed is as fast as that reported in recent publications. An optimized MATLAB code providing rapid computation with high accuracy is presented.
Highlights
IntroductionThe complex error function, known as the Faddeeva function, is given by: [1,2]. = e−z (1 + √2iπ 0 e−t dt), B.; Zhao, R.; Liu, Q.; Dai, M
The complex error function, known as the Faddeeva function, is given by: [1,2]Citation: Wang, Y.; Zhou, B.; Wang, w(z) = e−z erfc(−iz) Rz 2= e−z (1 + √2iπ 0 e−t dt), B.; Zhao, R.; Liu, Q.; Dai, M
In this work we propose a new algorithm for highly accurate evaluation of the Voigt/complex error function with small imaginary argument (y ≤ 0.1) based on the Taylor expansion method
Summary
The complex error function, known as the Faddeeva function, is given by: [1,2]. = e−z (1 + √2iπ 0 e−t dt), B.; Zhao, R.; Liu, Q.; Dai, M. Several high-accuracy algorithms, i.e., “fexp” [32,33], “voigtf” [34] and “fadsamp” [35], proposed by Abrarov and his collaborators were developed to achieve highly accurate and simultaneously rapid computation of Voigt/complex error function. Based on the Maclaurin expansion of the exponential function to overcome its notorious difficulty This approximation is sufficient for the most practical tasks, the more accurate yet efficient approximation for the Voigt and complex error function may be required in modern precision spectroscopy [37]. In this work we propose a new algorithm for highly accurate evaluation of the Voigt/complex error function with small imaginary argument (y ≤ 0.1) based on the Taylor expansion method.
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