On Nonlinear Urysohn Integral Equation Via Measures of Noncompactness and Numerical Method to Solve It

In this study, we present the existence of solutions for Urysohn integral equations. By using the techniques of noncompactness measures, we employ the basic fixed point theorems such as Petryshyn's fixed point theorem to obtain the mentioned aim in Banach algebra. Then this paper presents a numerical approach based on Haar wavelets to solve the equation. This numerical method does not lead to a nonlinear algebraic equations system. Conducting numerical experiments confirm the theoretical results of the applied method and endorse the accuracy of the method.