On the good modelling of certain growth processes
type: Item
instance of: scholarly article
title: On the good modelling of certain growth processes
zbMATH Open document ID: 1144.26004
author: Michael Bürker
published in: Mathematische Semesterberichte
publication date: 2007-03-20T00:00:00Z
review text: The author studies the relation between the continuous modelling (by a differential equation) of some growth processes and the corresponding discrete one. In order to show if the first one can be replaced by the second one without to commit a systematic error the author introduces the notion of ``step-stable'' functions \(f\) as the ones for which the quotient \((f(x+h)-f(x))/f'(x)h\) does not depend on \(x\), for all real \(x\) and \(h\neq 0\). It is shown that this is equivalent to state that \(f\) is of the form \(f(x)=mx +b\) or \(f(x)=ca^x+b\) (and satisfies a linear differential equation). The role of \(f\) is illustrated by some examples.
Mathematics Subject Classification ID: 26A12
zbMATH DE Number: 5135826
zbMATH Keywords: step-stable function
reviewed by: Vojislav Marić
MaRDI profile type: Publication
full work available at URL: s00591-006-0009-4
OpenAlex ID: W2087606391
cites work: Q3681276
cites work: Q4410766
DOI: 10.1007/S00591-006-0009-4
description: scientific article; zbMATH DE number 5135826