Nystrom method for Fredholm integral equations of the second kind in two variables on a triangle

The paper deals with the approximation of the solution of the following bivariate Fredholm integral equation $$ f(\Y)-\mu \int_\D \K(\X,\Y) f(\X) \widetilde\omega(\X) \ d\X = g(\Y), \quad \Y\in \D, $$ where the domain $\D$ is a triangle. The proposed procedure, by a suitable transformation, is essentially the Nystr\"om method based on the zeros of univariate Jacobi orthogonal polynomials. Convergence, stability and well conditioning of the method are proved. In order to illustrate the efficiency of the proposed method some numerical tests are given.