Computational methods for integral equations
Computational methods for integral equations
A class of bases in L2 for the sparse representations of integral operators
SIAM Journal on Mathematical Analysis
Superconvergence of the iterated Galerkin methods for Hammerstein equations
SIAM Journal on Numerical Analysis
Superconvergence of the iterated collocation methods for Hammerstein equations
Journal of Computational and Applied Mathematics
Multiwavelets for Second-Kind Integral Equations
SIAM Journal on Numerical Analysis
The Petrov--Galerkin and Iterated Petrov--Galerkin Methods for Second-Kind Integral Equations
SIAM Journal on Numerical Analysis
Fast Collocation Methods for Second Kind Integral Equations
SIAM Journal on Numerical Analysis
Harmonic wavelets towards the solution of nonlinear PDE
Computers & Mathematics with Applications
About a numerical method of successive interpolations for functional Hammerstein integral equations
Journal of Computational and Applied Mathematics
Wavelet Collocation Method and Multilevel Augmentation Method for Hammerstein Equations
SIAM Journal on Scientific Computing
Fast Multilevel Augmentation Methods for Nonlinear Boundary Integral Equations
SIAM Journal on Numerical Analysis
Review: Wavelet-based numerical analysis: A review and classification
Finite Elements in Analysis and Design
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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.