A collocation method for the numerical solution of a two dimensional integral equation using a quadratic spline quasi‐interpolant

In this paper, we propose an interesting method for approximating the solution of a two dimensional second kind equation with a smooth kernel using a bivariate quadratic spline quasi‐interpolant (abbr. QI) defined on a uniform criss‐cross triangulation of a bounded rectangle. We study the approximation errors of this method together with its Sloan’s iterated version and we illustrate the theoretical results by some numerical examples.