Numerical solution of non-linear Fredholm integral equations by using multiwavelets in the Petrov-Galerkin method

In this paper, we use the Wavelet Petrov-Galerkin (WPG) method for solving one of the most important cases in non-linear Fredholm integral equations which is called Hammerstein equations. We suppose that the trial space and the test space that are used in this method, to be piecewise polynomials space. Also we use Alpert's multiwavelets as the bases for these spaces, such that the wavelet basis for the test space constructed from lower degree polynomials than the trial space. Finally, for showing efficiency of this method, we use some numerical examples.