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

  • Andrzej MarciniakEmail author
  • Malgorzata A. Jankowska
  • Tomasz Hoffmann
Conference paper
  • 119 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, 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 

Notes

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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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Andrzej Marciniak
    • 1
    • 2
    Email author
  • Malgorzata A. Jankowska
    • 3
  • Tomasz Hoffmann
    • 4
  1. 1.Institute of Computing SciencePoznan University of TechnologyPoznanPoland
  2. 2.Department of Computer ScienceState University of Applied Sciences in KaliszKaliszPoland
  3. 3.Institute of Applied MechanicsPoznan University of TechnologyPoznanPoland
  4. 4.Poznan Supercomputing and Networking CenterPoznanPoland

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