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

Marciniak A.

Computational Methods in Science and Technology

2019

Vol. 25, No. 2

81--97

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. W˛e 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.

Solving the Poisson Equation by an Interval Difference Method of the Second Order

Hoffmann T., Marciniak A.

Computational Methods in Science and Technology

2013

Vol. 19, No. 1

13--21

The paper deals with an interval difference method for solving the Poisson equation based on the conventional central-difference method. We present the interval method in full details. The method is constructed in such a way that the exact solution is included in the interval solution obtained. Some numerical results obtained in ﬂoating-point interval arithmetic are also presented