Fixed point method for solving nonlinear quadratic Volterra integral equations

We consider a paper of Banas and Sadarangani (2008) which deals with monotonicity properties of the superposition operator and their applications. An application of the monotonicity properties is to study the solvability of a quadratic Volterra integral equation. In this paper, we prepare an efficient numerical technique based on the fixed point method and quadrature rules to approximate a solution for quadratic Volterra integral equation. Then convergence of numerical scheme is proved by some theorems and some numerical examples are given to show applicability and accuracy of the numerical method and guarantee the theoretical results.