Skip to main content
SpringerLink
Log in

On the Stability of Fully-Explicit Finite-Difference Scheme for Two-Dimensional Parabolic Equation with Nonlocal Conditions

  • Conference paper
Computational Science and Its Applications - ICCSA 2011 (ICCSA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6785))

Included in the following conference series:

Abstract

We construct and analyse a fully-explicit finite-difference scheme for a two-dimensional parabolic equation with nonlocal integral conditions. The main attention is paid to the stability of the scheme. We apply the stability analysis technique which is based on the investigation of the spectral structure of the transition matrix of a finite-difference scheme and demonstrate that depending on the parameters of nonlocal conditions the proposed method can be stable or unstable. The results of numerical experiment with one test problem are also presented and they validate theoretical results.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Atkinson, K.E.: An Introduction to Numerical Analysis. John Willey & Sons, New York (1978)

    MATH  Google Scholar 

  2. Cahlon, B., Kulkarni, D.M., Shi, P.: Stepwise stability for the heat equation with a nonlocal constraint. SIAM J. Numer. Anal. 32(2), 571–593 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  3. Dehghan, M.: Implicit locally one-dimensional methods for two-dimensional diffusion with a non-local boundary condition. Math. Comput. Simulat. 49(4–5), 331–349 (1999)

    Article  MathSciNet  Google Scholar 

  4. Jesevičiūtė, Ž., Sapagovas, M.: On the stability of finite-difference schemes for parabolic equations subject to integral conditions with applications to thermoelasticity. Comput. Methods Appl. Math. 8(4), 360–373 (2008)

    MathSciNet  MATH  Google Scholar 

  5. Sajavičius, S.: On the stability of alternating direction method for two-dimensional parabolic equation with nonlocal integral conditions. In: Kleiza, V., Rutkauskas, S., Štikonas, A. (eds.) Proceedings of International Conference Differential Equations and their Applications (DETA 2009), pp. 87–90. Panevėžys, Lithuania (2009)

    Google Scholar 

  6. Sajavičius, S.: The stability of finite-difference scheme for two-dimensional parabolic equation with nonlocal integral conditions. In: Damkilde, L., Andersen, L., Kristensen, A.S., Lund, E. (eds.) Proceedings of the Twenty Second Nordic Seminar on Computational Mechanics / DCE Technical Memorandum, vol. 11, pp. 87–90. Aalborg, Denmark (2009)

    Google Scholar 

  7. Sajavičius, S.: On the stability of locally one-dimensional method for two-dimensional parabolic equation with nonlocal integral conditions. In: Pereira, J.C.F., Sequeira, A., Pereira, J.M.C. (eds.) Proceedings of the V European Conference on Computational Fluid Dynamics (ECCOMAS CFD 2010). CD-ROM, Paper ID 01668, 11 p. Lisbon, Portugal (2010)

    Google Scholar 

  8. Sajavičius, S.: On the eigenvalue problems for differential operators with coupled boundary conditions. Nonlinear Anal., Model. Control 15(4), 493–500 (2010)

    MathSciNet  MATH  Google Scholar 

  9. Sajavičius, S.: On the eigenvalue problems for finite-difference operators with coupled boundary conditions. Šiauliai Math. Semin. 5(13), 87–100 (2010)

    MathSciNet  MATH  Google Scholar 

  10. Sajavičius, S., Sapagovas, M.: Numerical analysis of the eigenvalue problem for one-dimensional differential operator with nonlocal integral conditions. Nonlinear Anal., Model. Control 14(1), 115–122 (2009)

    MathSciNet  MATH  Google Scholar 

  11. Samarskii, A.A.: The Theory of Difference Schemes. Marcel Dekker Inc., New York–Basel (2001)

    Book  MATH  Google Scholar 

  12. Sapagovas, M.: On the stability of a finite-difference scheme for nonlocal parabolic boundary-value problems. Lith. Math. J. 48(3), 339–356 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. Sapagovas, M.P.: On stability of finite-difference schemes for one-dimensional parabolic equations subject to integral condition. Obchysl. Prykl. Mat. 92, 77–90 (2005)

    Google Scholar 

  14. Sapagovas, M., Kairytė, G., Štikonienė, O., Štikonas, A.: Alternating direction method for a two-dimensional parabolic equation with a nonlocal boundary condition. Math. Model. Anal. 12(1), 131–142 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  15. Yang, W.Y., Cao, W., Chung, T.-S., Morris, J.: Applied Numerical Methods Using MATLAB®. John Willey & Sons, New York (2005)

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Vilnius University, Naugarduko str. 24, LT-03225, Vilnius, Lithuania

    Svajūnas Sajavičius

  2. Mykolas Romeris University, Ateities str. 20, LT-08303, Vilnius, Lithuania

    Svajūnas Sajavičius

Authors
  1. Svajūnas Sajavičius
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Basilicata University Potenza, L.I.S.U.T. - D.A.P.I.T., 10, Viale dell’Ateneo Lucano, 85100, Potenza, Italy

    Beniamino Murgante

  2. Department of Mathematics and Computer Science, University of Perugia, Via Vanvitelli, 1, 06123, Perugia, Italy

    Osvaldo Gervasi

  3. Department of Applied Mathematics and Computational Sciences, University of Cantabria, Avda. de los Castros, s/n, Santander, C.P. 39005, Spain

    Andrés Iglesias

  4. School of Business Systems, Monash University, VIC 3800, Clayton, Australia

    David Taniar

  5. Department of Intelligent Informatics, Kyushu Sangyo University, 2-3-1 Matsukadai, Higashi-ku, 813-8503, Fukuoka, Japan

    Bernady O. Apduhan

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Sajavičius, S. (2011). On the Stability of Fully-Explicit Finite-Difference Scheme for Two-Dimensional Parabolic Equation with Nonlocal Conditions. In: Murgante, B., Gervasi, O., Iglesias, A., Taniar, D., Apduhan, B.O. (eds) Computational Science and Its Applications - ICCSA 2011. ICCSA 2011. Lecture Notes in Computer Science, vol 6785. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21898-9_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-21898-9_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21897-2

  • Online ISBN: 978-3-642-21898-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation