Computing Fresnel integrals via modified trapezium rules

@article{Alazah2014ComputingFI,
  title={Computing Fresnel integrals via modified trapezium rules},
  author={Mohammad Alazah and Simon N. Chandler-Wilde and Scott La Porte},
  journal={Numerische Mathematik},
  year={2014},
  volume={128},
  pages={635-661}
}
In this paper we propose methods for computing Fresnel integrals based on truncated trapezium rule approximations to integrals on the real line, these trapezium rules modified to take into account poles of the integrand near the real axis. Our starting point is a method for computation of the error function of complex argument due to Matta and Reichel (J Math Phys 34:298–307, 1956) and Hunter and Regan (Math Comp 26:539–541, 1972). We construct approximations which we prove are exponentially… CONTINUE READING
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