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An Interval Difference Method of Second Order for Solving an Elliptical BVP

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 12044)

Abstract

In the article we present an interval difference scheme for solving a general elliptic boundary value problem with Dirichlet’ boundary conditions. The obtained interval enclosure of the solution contains all possible numerical errors. A numerical example we present confirms that the exact solution belongs to the resulting interval enclosure.

Keywords

  • Interval difference methods
  • Elliptic boundary value problem
  • Floating-point interval arithmetic

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  • DOI: 10.1007/978-3-030-43222-5_36
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Fig. 1.

Notes

  1. 1.

    There is also known directed interval arithmetic in which the left-ends of intervals may be greater than the right-end of ones. But it is not the case of our paper – we use only proper intervals.

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Acknowledgments

The paper was supported by the Poznan University of Technology (Poland) through the Grants No. 09/91/DSPB/1649 and 02/21/ SBAD/3558.

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Correspondence to Andrzej Marciniak .

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Marciniak, A., Jankowska, M.A., Hoffmann, T. (2020). An Interval Difference Method of Second Order for Solving an Elliptical BVP. In: Wyrzykowski, R., Deelman, E., Dongarra, J., Karczewski, K. (eds) Parallel Processing and Applied Mathematics. PPAM 2019. Lecture Notes in Computer Science(), vol 12044. Springer, Cham. https://doi.org/10.1007/978-3-030-43222-5_36

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  • DOI: https://doi.org/10.1007/978-3-030-43222-5_36

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