APPLICATION OF FIXED POINT METHOD FOR SOLVING NONLINEAR VOLTERRA-HAMMERSTEIN INTEGRAL EQUATION

There are various numerical methods to solve nonlinear integral equations. Most of them transform the integral equation into a system of nonlinear algebraic equations. It is cumbersome to solve these systems, or the solution may be unreliable. In this paper, we study the application of the fixed point method to solve Volterra-Hammerstein integral equations. This method does not lead to a nonlinear algebraic equations system. We show how the proper conditions guarantee the uniqueness of the solution and how the fixed point method approximates this solution. A bound for the norm of the error is derived and our results prove the convergence of the method. Finally, we present numerical examples which confirm our approach.