On the Highly Accurate Evaluation of the Voigt/Complex Error Function with Small Imaginary Argument

Yihong Wang, Bin Zhou, Bubin Wang, Rong Zhao, Qi Liu and Minglu Dai
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Yihong Wang: School of Energy and Environment, Southeast University, Nanjing 210096, China
Bin Zhou: School of Energy and Environment, Southeast University, Nanjing 210096, China
Bubin Wang: School of Energy and Environment, Southeast University, Nanjing 210096, China
Rong Zhao: School of Energy and Environment, Southeast University, Nanjing 210096, China
Qi Liu: School of Energy and Environment, Southeast University, Nanjing 210096, China
Minglu Dai: School of Energy and Environment, Southeast University, Nanjing 210096, China

Mathematics, 2022, vol. 10, issue 3, 1-13

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.

Keywords: Voigt function; complex error function; high-accuracy approximation; Taylor expansion (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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