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

• Autorzy: Marciniak A.

Identyfikatory

DOI

10.12921/cmst.2019.0000016

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Nakao’s method; interval difference method; elliptic boundary value problem; floating point interval arithmetic

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2019
• Tom: Vol. 25, No. 2
• Strony: 81--97
• Opis fizyczny: Bibliogr. 18 poz., rys.

Twórcy

autor

Marciniak A.

• Institute of Computing Science Poznań University of Technology Piotrowo 2, 60-965 Poznań, Poland
• Department of Computer Science State University of Applied Sciences in Kalisz Poznańska 201-205, 62-800 Kalisz, Poland

Bibliografia

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• [10] E. Süli, Lecture Notes on Finite Element Methods for Partial Differential Equations, University of Oxford (2000).https://people.maths.ox.ac.uk/suli/fem.pdf
• [11] T. Hoffmann, A. Marciniak, Solving the Generalized Poisson Equation in Proper and Directed Interval Arithmetic, Computational Methods in Science and Technology 22(4), 225–232 (2016).
• [12] T. Hoffmann, A. Marciniak, B. Szyszka, Interval Versions of Central Difference Method for Solving the Poisson Equation in Proper and Directed Interval Arithmetic, Foundations of Computing and Decision Sciences 38(3), 193–206 (2013).
• [13] T. Hoffmann, A. Marciniak, Solving the Poisson Equation by an Interval Method of the Second Order, Computational Methods in Science and Technology 19(1), 13–21 (2013).
• [14] A. Marciniak, T. Hoffmann, Interval Difference Methods for Solving the Poisson Equation, [In:] S. Pinelas, T. Caraballo, P. Kloeden, J.R. Graef (eds.), Differential and Difference Equations with Applications, vol. 230 of Springer Proceedings in Mathematics & Statistics, 259–270, Springer (2018).
• [15] A. Marciniak, An Interval Difference Method for Solving the Poisson Equation – the First Approach, Pro Dialog 24, 49–61 (2008).
• [16] A. Marciniak, Interval Arithmetic Unit, (2016). http://www.cs.put.poznan.pl/amarciniak/IAUnits/IntervalArithmetic32and64.pas
• [17] R.E. Moore, R.B. Kearfott, M.J. Cloud, Introduction to Interval Analysis, SIAM, Philadelphia (2009).
• [18] A. Marciniak, Delphi Pascal Programs for Nakao and Interval Difference Methods for Solving the Elliptic BVP, (2019).http://www.cs.put.poznan.pl/amarciniak/NIDM-EllipticBVP-Examples

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).