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APPROXIMATING THE KOHLRAUSCH FUNCTION BY SUMS OF EXPONENTIALS
- Part of
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- Journal:
- The ANZIAM Journal / Volume 54 / Issue 4 / April 2013
- Published online by Cambridge University Press:
- 04 September 2013, pp. 306-323
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- Article
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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.
