A numerical method for the generalized Love integral equation in 2D

This paper deals with the numerical solution of the generalized Love integral equation defined on the square. The method is of Nyström type and is based on the approximation of the integral by a product cubature rule whose coefficients are approximated by a “dilation” scheme. The theoretical analysis of the presented method is discussed by proving its stability and convergence in weighted spaces equipped with the uniform norm. To support the theoretical estimates, some numerical tests are presented.