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

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  • Abrarov, Sanjar M.
  • Quine, Brendan M.

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 ∼10−14 in the domain of practical importance 0≤y<0.1∩|x+iy|≤8. A Matlab code for computation of the complex error function with entire coverage of the complex plane is presented.

Suggested Citation

  • Abrarov, Sanjar M. & Quine, Brendan M., 2018. "A rational approximation of the Dawson’s integral for efficient computation of the complex error function," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 526-543.
    • Handle: RePEc:eee:apmaco:v:321:y:2018:i:c:p:526-543
    DOI: 10.1016/j.amc.2017.10.032
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    References listed on IDEAS

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    1. Abrarov, S.M. & Quine, B.M., 2015. "Sampling by incomplete cosine expansion of the sinc function: Application to the Voigt/complex error function," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 425-435.
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    Cited by:

    1. Sanjar M. Abrarov & Rehan Siddiqui & Rajinder K. Jagpal & Brendan M. Quine, 2022. "A Two-Domain MATLAB Implementation for Efficient Computation of the Voigt/Complex Error Function," Mathematics, MDPI, vol. 10(19), pages 1-14, September.
    2. S. M. Abrarov & B. M. Quine & R. Siddiqui & R. K. Jagpal, 2019. "A Single-Domain Implementation of the Voigt/Complex Error Function by Vectorized Interpolation," Earth Science Research, Canadian Center of Science and Education, vol. 8(2), pages 1-52, February.

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    1. S. M. Abrarov & B. M. Quine & R. Siddiqui & R. K. Jagpal, 2019. "A Single-Domain Implementation of the Voigt/Complex Error Function by Vectorized Interpolation," Earth Science Research, Canadian Center of Science and Education, vol. 8(2), pages 1-52, February.
    2. Sanjar M. Abrarov & Rehan Siddiqui & Rajinder K. Jagpal & Brendan M. Quine, 2022. "A Two-Domain MATLAB Implementation for Efficient Computation of the Voigt/Complex Error Function," Mathematics, MDPI, vol. 10(19), pages 1-14, September.

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