Wavelet applications to the Petrov–Galerkin method for Hammerstein equations

The purpose of this paper is two-fold. First, we develop the Petrov–Galerkin method and the iterated Petrov–Galerkin method for a class of nonlinear Hammerstein equations. Alpert [SIAM J. Math. Anal. 24 (1993) 246] established a class of wavelet basis and applied it to approximate solutions of the F...

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Bibliographic Details
Published in:Applied numerical mathematics 2003-05, Vol.45 (2), p.255-273
Main Authors: Kaneko, Hideaki, Noren, Richard D., Novaprateep, Boriboon
Format: Article
Language:English
Subjects:
Exact sciences and technology
Integral equations, integral transforms
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
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Summary:The purpose of this paper is two-fold. First, we develop the Petrov–Galerkin method and the iterated Petrov–Galerkin method for a class of nonlinear Hammerstein equations. Alpert [SIAM J. Math. Anal. 24 (1993) 246] established a class of wavelet basis and applied it to approximate solutions of the Fredholm second kind integral equations by the Galerkin method. He then demonstrated an advantage of a wavelet basis application to such equations by showing that the corresponding linear system is sparse. The second purpose of this paper is to study how this advantage of the sparsity can be extended to nonlinear Hammerstein equations.
ISSN:0168-9274
1873-5460
DOI:10.1016/S0168-9274(02)00173-3