Approximating the Kohlrausch function by sums of exponentials

Authors

  • Min Zhong School of Mathematical Sciences, Fudan University, 200433 Shanghai, People’s Re- public of China.
  • Richard Loy Mathematical Sciences Institute, Australian National University, Canberra, ACT 0200/ Australia
  • Robert Anderssen CSIRO Mathematics, Informatics and Statistics, GPO Box 664, Canberra, ACT 2601/ Australia

DOI:

https://doi.org/10.21914/anziamj.v54i0.5539

Keywords:

Kohlrausch function, sums of exponentials, approximation

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

Published

2013-10-16

Issue

Vol. 54 (2012)

Section

Articles for Printed Issues