Superconsistent discretizations of integral type equations Original Research Article

We recall some of the results, obtained by using the collocation method at special nodes, in the approximation of boundary value problems for partial differential equations. Similar techniques are applied for discretizing, by the Gaussian collocation method, a singular integral equation of the Carleman type. The idea, documented by some comparative tests, can be generalized to other approximation methods and/or integral equations of a different kind. It can also provide a link between different numerical approaches.