Über die näherungsweise Lösung nichtlinearer Integralgleichungen

Summary In this paper we study the iterative solvability of nonlinear systems of equations which arise from the discretization of Hammerstein integral equations. It is shown that, for a large class of equations satisfying monotonicity assumptions, it is possible to solve these systems by means of a linearly convergent iteration method. Moreover, for general monotone operators on a Hilbert space a globally convergent variant of Newton's method is given. Finally it is shown that this method effectively can be applied in a natural way to the systems of equations under consideration.