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Identification of partial differential equation models for a class of multiscale spatio-temporal dynamical systems

Guo, L.Z., Billings, S.A. and Coca, D. (2006) Identification of partial differential equation models for a class of multiscale spatio-temporal dynamical systems. Research Report. ACSE Research Report no. 945 . Automatic Control and Systems Engineering, University of Sheffield

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Abstract

In this paper, the identification of a class of multiscale spatio-temporal dynamical sys-tems, which incorporate multiple spatial scales, from observations is studied. The proposed approach is a combination of Adams integration and an orthogonal least squares algorithm, in which the multiscale operators are expanded, using polynomials as basis functions, and the spatial derivatives are estimated by finite difference methods. The coefficients of the polynomials can vary with respect to the space domain to represent the feature of multiple scales involved in the system dynamics and are approximated using a B-spline wavelet multi-resolution analysis (MRA). The resulting identified models of the spatio-temporal evolution form a system of partial differential equations with different spatial scales. Examples are provided to demonstrate the efficiency of the proposed method.

Item Type: Monograph (Research Report)
Copyright, Publisher and Additional Information: The Department of Automatic Control and Systems Engineering research reports offer a forum for the research output of the academic staff and research students of the Department at the University of Sheffield. Papers are reviewed for quality and presentation by a departmental editor. However, the contents and opinions expressed remain the responsibility of the authors. Some papers in the series may have been subsequently published elsewhere and you are advised to cite the later published version in these instances.
Institution: The University of Sheffield
Academic Units: The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Automatic Control and Systems Engineering (Sheffield) > ACSE Research Reports
Depositing User: Miss Anthea Tucker
Date Deposited: 10 Oct 2012 10:42
Last Modified: 05 Jun 2014 12:48
Status: Published
Publisher: Automatic Control and Systems Engineering, University of Sheffield
URI: http://eprints.whiterose.ac.uk/id/eprint/74604

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