Nakao’s method and an interval difference scheme of second order for solving the elliptic BVP

Abstract

In the paper we compare Nakao's method to our interval difference scheme of second order. Repeating some computational examples of Nakao, we have observed that our implementation of his method gives better results. Moreover, it appears that the presented interval difference scheme gives better enclosures of exact solutions than Nakao's method. Wę also point out that the considered interval method can be used to solve the Poisson equation with Dirichlet's condition, for which Nakao's method is not applicable.