Wavelet applications to the Petrov--Galerkin method for Hammerstein equations (Q1874218)

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.