Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
On Asymptotic Behavior of Blow-Up Solutions to Higher-Order Differential Equations with General Nonlinearity Read chapter Read first chapter

2018 | OriginalPaper | Chapter

Interval Difference Methods for Solving the Poisson Equation

Authors : Andrzej Marciniak, Tomasz Hoffmann

Published in: Differential and Difference Equations with Applications

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In the paper we resemble interval difference method of second order designed by us earlier and present new, fourth order interval difference methods for solving the Poisson equation with Dirichlet boundary conditions. Interval solutions obtained contain all possible numerical errors. Numerical solutions presented confirm the fact that the exact solutions are within the resulting intervals.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Conjecture on Fučík Curve Asymptotes for a Particular Discrete Operator
next chapter Gevrey Well Posedness of Goursat-Darboux Problems and Asymptotic Solutions
Footnotes
1
In our opinion, it is rather impossible to obtain a theoretical proof of this fact.
 
Literature
1.
Alefeld, G., Herzberger, J.: Introduction to Interval Computations. Academic Press, New York (1983)MATH
2.
Burden, R.L., Faires, J.D.: Numerical Analysis, 3rd edn. Weber & Schmidt Publishers, Prindle (1985)MATH
3.
Hammer, R., Hocks, M., Kulisch, U., Ratz, D.: Numerical Toolbox for Verified Computing I. Basic Numerical Problems, Theory, Algorithms, and Pascal-XSC Programs. Springer, Berlin (1993)MATH
4.
Hansen, E.R.: Topics in Interval Analysis. Oxford University Press, London (1969)MATH
5.
Harfash, A.J., Jalob, H.A.: Sixth and fourth order compact finite difference schemes for two and three dimension poisson equation with two methods to derive these schemes. Basrah J. Sci. 2, 1–20 (2006)
6.
Hoffmann, T., Marciniak, A.: Solving the poisson equation by an interval difference method of the second order. Comput. Methods Sci. Technol. 19(1), 13–21 (2013)CrossRef
7.
Hoffmann, T., Marciniak, A.: Solving the generalized poisson equation in proper and directed interval arithmetic. Comput. Methods Sci. Technol. 22(4), 225–232 (2016)CrossRef
8.
Hoffmann, T., Marciniak, A., Szyszka, B.: Interval versions of central difference method for solving the poisson equation in proper and directed interval arithmetic. Found. Comput. Decis. Sci. 38(3), 193–206 (2013)MathSciNetMATH
9.
Kincaid, D.R., Cheney, E.W.: Numerical analysis: mathematics of scientific computing, 3rd edn. American Mathematical Society, Providence (2002)MATH
10.
Marciniak, A.: An interval difference method for solving the poisson equation the first approach. Pro Dialog 24, 49–61 (2008)
11.
12.
13.
14.
Meis, T., Marcowitz, U.: Numerical Solution of Partial Differential Equations. Springer, Berlin (1981)CrossRef
15.
Moore, R.E.: Interval Analysis. Prentice-Hall, Englewood Cliffs (1966)MATH
16.
Moore, R.E.: Methods and Applications of Interval Analysis. SIAM, Philadelphia (1979)CrossRef
17.
Nakao, M.T.: On verified computations of solutions for nonlinear parabolic problems. IEICE Nonlinear Theory Appl. 5(3), 320–338 (2014)CrossRef
18.
Popova, E.D.: Extended interval arithmetic in IEEE floating-point environment. Interval Comput. 4, 100–129 (1994)MathSciNetMATH
19.
Zhang, J.: Multigrid method and fourth-order compact scheme for 2D poisson equation with unequal mesh- size discretization. J. Comput. Phys. 179, 170–179 (2002)CrossRef
Metadata
Title
Interval Difference Methods for Solving the Poisson Equation
Authors
Andrzej Marciniak
Tomasz Hoffmann
Copyright Year
2018
Book
Differential and Difference Equations with Applications

Print ISBN: 978-3-319-75646-2

Electronic ISBN: 978-3-319-75647-9

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-75647-9_21

Premium Partner

    Image Credits