On the numerical treatment and analysis of two-dimensional Fredholm integral equations using quasi-interpolant

Abstract

In this paper, we study the quadratic rule for the numerical solution of linear and nonlinear two-dimensional Fredholm integral equations based on spline quasi-interpolant. Also the convergence analysis of the method is given. We show that the order of the method is $$O(h_{x}^{m+1})+O(h_{y}^{m^{\prime }+1})$$. The theoretical behavior is tested on examples and it is shown that the numerical results confirm theoretical part.