Wavelet applications to the Petrov–Galerkin method for Hammerstein equations Original Research Article

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.