Solving nonlinear integral equations in the Urysohn form by Newton-Kantorovich-quadrature method
The Newton-Kantorovich method is a well-known method for solving nonlinear integral equations. This method attempts to solve a sequence of linear integral equations. In this article, we develop a new method, which is a combination of the Newton-Kantorovich and quadrature methods. The new method solves the nonlinear integral equations of the Urysohn form in a systematic procedure. Some numerical examples are provided, and the obtained numerical approximations are compared with the corresponding exact solutions. (C) 2010 Elsevier Ltd. All rights reserved.
nonlinear integral equation quadrature newton-kantorovich method urysohn integral equation