Approximating the Kohlrausch function by sums of exponentials

Min Zhong, Richard Loy, Robert Anderssen

Abstract


The Kohlrausch functions \(\exp(−t\beta)\), with \(\beta\in (0, 1)\), which are important in a wide range of physical, chemical and biological applications, correspond to specific realizations of completely monotone functions. In this paper, using nonuniform grids and midpoint estimates, constructive procedures are formulated and analysed for the Kohlrausch functions. Sharper estimates are discussed to improve the approximation results. Numerical results and representative approximations are presented to illustrate the effectiveness of the proposed method.

doi:10.1017/S1446181113000229

Keywords


Kohlrausch function, sums of exponentials, approximation



DOI: http://dx.doi.org/10.21914/anziamj.v54i0.5539



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.