Optimal quadrature rules for numerical solution of the nonlinear Fredholm integral equations

Abstract

In this paper, an iterative method of successive approximations to the approximate solution of
nonlinear Hammerstein- Fredholm integral equations using an optimal quadrature formula for classes
of functions of Lipschitz types, is provided. Also, the convergence analysis and numerical stability of
the proposed method are proved. Finally, some numerical examples verify the theoretical results and
show the accuracy of the method.