A modification for solving Fredholm‐Hammerstein integral equation by using wavelet basis

The purpose of this paper is to use Alpert wavelet basis and modify the integrand function approximation coefficients to solve Fredholm‐Hammerstein integral equations.

L²[0, 1] was considered as solution space and the solution was projected to the subspaces of L²[0, 1] with finite dimension so that basis elements of these subspaces were orthonormal.

In this process, solution of Fredholm‐Hammerstein integral equation is found by solving the generated system of nonlinear equations.

Comparing the method with others shows that this system has less computation. In fact, decreasing of computations result from the modification.