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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Yihong Wang & Bin Zhou & Bubin Wang & Rong Zhao & Qi Liu & Minglu Dai, 2022. "On the Highly Accurate Evaluation of the Voigt/Complex Error Function with Small Imaginary Argument," Mathematics, MDPI, vol. 10(3), pages 1-13, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:308-:d:728602
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