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

Wuttke, Joachim

doi:10.3390/a5040604

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

Joachim Wuttke

Forschungszentrum Jülich GmbH, Jülich Centre for Neutron Science at FRM II, Lichtenbergstraße 1, 85747 Garching, Germany

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

Received: 12 October 2012 / Revised: 13 November 2012 / Accepted: 14 November 2012 / Published: 22 November 2012

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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(-t^β) 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. View Full-Text

Keywords: stretched exponential; Laplace–Fourier transform; numeric integration

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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. https://doi.org/10.3390/a5040604

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. https://doi.org/10.3390/a5040604

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. https://doi.org/10.3390/a5040604

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

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