Wavelet applications to the Petrov--Galerkin method for Hammerstein equations
type: Item
instance of: scholarly article
title: Wavelet applications to the Petrov--Galerkin method for Hammerstein equations
zbMATH Open document ID: 1019.65106
DOI: 10.1016/S0168-9274(02)00173-3
author: Hideaki Kaneko
author: Richard D. Noren
author: Boriboon Novaprateep
published in: Applied Numerical Mathematics
publication date: 2003-05-22T00:00:00Z
review text: In the first part the authors develop the Petrov-Galerkin method and the iterated Petrov-Galerkin method for a class of nonlinear Hammerstein equations. A class of wavelet bases is used with the Petrov-Galerkin method for solving a second kind Fredholm integral equation. In the second part of this paper, the authors study how the sparsity can be extended to nonlinear Hammerstein equations. A wavelet application to such equations allows to prove that the corresponding linear system is sparse. This paper is only theoretical. It may be noted that nonlinear Hammerstein equations can be easily solved by means of the Adomian decomposition method. This method allows to find a mathematical solution (series) explicitly dependent on the initial variables and parameters arising in the equation.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 1915293
zbMATH Keywords: wavelets
zbMATH Keywords: Petrov-Galerkin method
zbMATH Keywords: nonlinear Hammerstein equations
zbMATH Keywords: second kind Fredholm integral equation
zbMATH Keywords: Adomian decomposition method
reviewed by: Yves Cherruault
MaRDI profile type: Publication
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full work available at URL: s0168-9274(02)00173-3
OpenAlex ID: W2024654917
description: scientific article; zbMATH DE number 1915293