In this paper, a review of new works on approximate methods for solving nonlinear Fredholm integral equations of the second kind is carried out. Legendre wavelets are used for the numerical solution of nonlinear Fredholm integral equations of the second kind by the Galerkin-Bubnov projection method. The Newton-Kantorovich method for a system of nonlinear algebraic equations is considered and numerical calculations are carried out. The comparative analysis shows that the Bubnov-Galerkin method with basic functions in the form of Legendre wavelets is effective in terms of accuracy and convenient to implement.
keywords: nonlinear Fredholm integral equations of the second kind, Legendre wavelets, Galerkin-Bubnov method, Newton’s method.
