Algorithms 2012, 5(4), 604-628; doi:10.3390/a5040604
Article

Laplace–Fourier Transform of the Stretched Exponential Function: Analytic Error Bounds, Double Exponential Transform, and Open-Source Implementation “libkww”

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Received: 12 October 2012; in revised form: 13 November 2012 / Accepted: 14 November 2012 / Published: 22 November 2012
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract: The C library libkww provides functions to compute the Kohlrausch–Williams– Watts function, i.e., the Laplace–Fourier transform of the stretched (or compressed) exponential function exp(-tβ ) for exponents β between 0.1 and 1.9 with double precision. Analytic error bounds are derived for the low and high frequency series expansions. For intermediate frequencies, the numeric integration is enormously accelerated by using the Ooura–Mori double exponential transformation. The primitive of the cosine transform needed for the convolution integrals is also implemented. The software is hosted at http://apps.jcns.fz-juelich.de/kww; version 3.0 is deposited as supplementary material to this article.
Keywords: stretched exponential; Laplace–Fourier transform; numeric integration
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MDPI and ACS Style

Wuttke, J. Laplace–Fourier Transform of the Stretched Exponential Function: Analytic Error Bounds, Double Exponential Transform, and Open-Source Implementation “libkww”. Algorithms 2012, 5, 604-628.

AMA Style

Wuttke J. Laplace–Fourier Transform of the Stretched Exponential Function: Analytic Error Bounds, Double Exponential Transform, and Open-Source Implementation “libkww”. Algorithms. 2012; 5(4):604-628.

Chicago/Turabian Style

Wuttke, Joachim. 2012. "Laplace–Fourier Transform of the Stretched Exponential Function: Analytic Error Bounds, Double Exponential Transform, and Open-Source Implementation “libkww”." Algorithms 5, no. 4: 604-628.

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