Moving averages of ordinary differential equations via convolution
type: Item
instance of: scholarly article
title: Moving averages of ordinary differential equations via convolution
zbMATH Open document ID: 1219.34059
author: Ido Bright
published in: Journal of Differential Equations
publication date: 2011-01-14T00:00:00Z
review text: The averaging method of ordinary differential equations approximates the solution of a time-varying system with a small amplitude on a long time domain, by the solution of an auxiliary time-invariant system. The paper establishes a different approach to the averaging method that works under conditions that are not covered by the standard method, for instance, the existence of the time average is not required. Namely, the paper introduces an averaging framework, where the solution of a time-varying equation with small amplitude is approximated by the solution of a slowly-varying auxiliary system, generated by convolving the original equation with a kernel function. The effect of the convolution is a smoothing of the equation, thus, making it more amenable to numerical computations. Results on the approximation error for general classes of vector fields and kernels are presented.
reviewed by: Eugene Ershov
Mathematics Subject Classification ID: 34C29
zbMATH DE Number: 5836850
zbMATH Keywords: averaging method of ordinary differential equations
zbMATH Keywords: time-varying averages
MaRDI profile type: Publication
full work available at URL: j.jde.2010.10.011
OpenAlex ID: W2035302232
cites work: Q5617898
cites work: Q4040102
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DOI: 10.1016/J.JDE.2010.10.011
description: scientific article; zbMATH DE number 5836850