Application of the decomposition method to identify the distributed parameters of an elliptical equation
type: Item
instance of: scholarly article
title: Application of the decomposition method to identify the distributed parameters of an elliptical equation
zbMATH Open document ID: 0822.65120
DOI: 10.1016/0895-7177(95)00006-N
author: S. Guellal
author: Yves Cherruault
published in: Mathematical and Computer Modelling
publication date: 1995-10-15T00:00:00Z
review text: \textit{G. Adomian} [Math. Comput. Modelling 13, No. 7, 17-43 (1990; Zbl 0713.65051)] has proposed to solve a nonlinear equation \(u= G(u)+ f\) (\(G\) operator from Hilbert space \(H\) to \(H\)) through an infinite series \(u= \sum u_ n\) with \(u_ 0= f\), \(u_{n+ 1}= A(u_ 0, u_ 1, \dots, u_ n)\), \(n\geq 0\), \(A\) polynomial. The authors show how the method yields the solution (approximated by truncation of the series \(u\)) of a special second-order elliptic boundary value problem in the unit square and a related inverse problem (determination of a coefficient in the equation). The equation is special, indeed, however, the efficiency is surprising. The authors hope to apply this technique to identification problems in biology and medicine, see e.g. their work in Math. Comput. Modelling 18, No. 8, 77-82 (1993; Zbl 0792.92009).
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 751285
zbMATH Keywords: decomposition method
zbMATH Keywords: parameter identification
zbMATH Keywords: nonlinear equation
zbMATH Keywords: Hilbert space
zbMATH Keywords: second-order elliptic boundary value problem
zbMATH Keywords: inverse problem
reviewed by: E. Lanckau
MaRDI profile type: Publication
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full work available at URL: 0895-7177(95)00006-n
OpenAlex ID: W2043342811
description: scientific article; zbMATH DE number 751285