Fully discrete approximation methods for the estimation of parabolic systems and boundary parameters
type: Item
instance of: scholarly article
title: Fully discrete approximation methods for the estimation of parabolic systems and boundary parameters
zbMATH Open document ID: 0611.65082
DOI: 10.1007/BF00046975
author: I. G. Rosen
author: H. Thomas Banks
published in: Acta Applicandae Mathematicae
publication date: 1986-01-01T00:00:00Z
review text: A spatially and temporally discrete approximation scheme is developed for the identification of a class of semilinear parabolic systems with unknown boundary parameters. The identification problem is formulated as a least squares fit to data subject to an equivalent representation for the dynamics in the form of an abstract evolution equation. An approximation method, based on Galerkin's method with cubic splines and Padé approximation of exponentials, is constructed. A sequence of approximating identification problems results, the solutions of which are shown to exist, and in a certain sense approximate solutions of the original identification problem. Numerical results for two examples, both based on actual experimental data, are included.
reviewed by: Michael Sever
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35R30
zbMATH DE Number: 3988670
zbMATH Keywords: inverse problems
zbMATH Keywords: numerical example
zbMATH Keywords: boundary parameter identification
zbMATH Keywords: semilinear parabolic systems
zbMATH Keywords: least squares fit
zbMATH Keywords: abstract evolution equation
zbMATH Keywords: Galerkin's method
zbMATH Keywords: cubic splines
zbMATH Keywords: Padé approximation of exponentials
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00046975
OpenAlex ID: W2074368798
description: scientific article; zbMATH DE number 3988670