A Newton-like iterative process for the numerical solution of Fredholm nonlinear integral equations (Q2568924)

The author proposes a Newton-like iterative method for the numerical solution of a second kind nonlinear Fredholm integral equation. This method is based on Picard iteration and on the Newton-Kantorovich method by using a degenerate kernel as an approximation of the kernel and also using an approximation for the Fréchet derivative of the nonlinear operator defined by the integral equation. A semi-local convergence result is proved. In Section 3 a practical construction of the operator involved in the iterative method and of its inverse is presented. Using the new iterative method, two numerical examples are performed.