Informatics and Applications
2017, Volume 11, Issue 4, pp 94-103
THE USE OF WAVELETS FOR THE CALCULATION OF LINEAR CONTROL SYSTEMS WITH LUMPED PARAMETERS
- Yu. I. Bityukov
- E. N. Platonov
Abstract
In many disciplines, problems appear which can be formulated with the aid of differential or integral equations. In simpler cases, such equations can be solved analytically, but for more complicated cases, numerical procedures are needed. In recent times, the wavelet-based methods have gained great popularity, where different wavelet families such as Daubechies, Coiflet, etc. wavelets are applied. A shortcoming of these wavelets is that they do not have an analytic expression. For this reason, differentiation and integration of these wavelets are very complicated. The paper presents algorithms for the numerical solution of linear integral and differential equations based on spline wavelets on the interval. The algorithms generalize the well-known methods based on Haar wavelets, which are a particular case of spline wavelets. The results presented can be applied for the analysis of linear systems with lumped parameters.
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[+] About this article
Title
THE USE OF WAVELETS FOR THE CALCULATION OF LINEAR CONTROL SYSTEMS WITH LUMPED PARAMETERS
Journal
Informatics and Applications
2017, Volume 11, Issue 4, pp 94-103
Cover Date
2017-12-30
DOI
10.14357/19922264170412
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
spline wavelet; differential equation; integral equation
Authors
Yu. I. Bityukov  and E. N. Platonov
Author Affiliations
Moscow Aviation Institute (National Research University), 4 Volokolamskoye Highway, Moscow 125993, Russian Federation
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