Two methods based on bivariate spline quasi-interpolants for solving Fredholm integral equations

For solving a Fredholm integral equation of the second kind, we approximate its kernel by two types of bivariate spline quasi-interpolants, namely the tensor product and the continuous blending sum of univariate spline quasi-interpolants. We give the construction of the approximate solutions, and we prove some theoretical results related to the approximation errors of these methods. We illustrate the obtained results by some numerical tests giving a comparison with several methods in the literature.