SpringerLink
Log in

On a general method for investigation of finite difference schemes

  • Published:
Lithuanian Mathematical Journal Aims and scope Submit manuscript

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (France)

Instant access to the full article PDF.

Institutional subscriptions

References

  1. C.D. Akrivis, V. A. Dougalis and O. A. Karakashian, On fully-discrete Galerkin methods of second order temporal accuracy for the nonlinear Schrödinger equation,Numer. Math.,59, 34–41 (1991).

    Article  MathSciNet  Google Scholar 

  2. Y. Tourigny, OptimalH 1 estimates for two time discrete Galerkin approximations of a nonlinear Schrödinger equation,IMA J. Numer. Anal.,11, 509–523 (1991).

    Article  MathSciNet  MATH  Google Scholar 

  3. H. J. Stetter,Analysis of Discretization Methods For Ordinary Differential Equations, Springer-Verlag, Berlin (1973).

    MATH  Google Scholar 

  4. K. Dekker and J. G. Verwer,Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations, North-Holland (1984).

  5. A. M. Stuart and A. R. Humphries, Model problems in numerical stability theory for initial value problems,SIAM Review,36, 226–257 (1994).

    Article  MathSciNet  MATH  Google Scholar 

  6. V. Thomee,Galerkin Method for Parabolic Problems, Lecture Notes in Mathematics, Springer-Verlag, Berlin (1984).

    Google Scholar 

  7. J. M. Sanz-Serna, Stability and convergence in numerical analysis, in:Linear Problems, a Simple, Comprehensive Account, J. K. Hale and P. Martinez-Aneores (Eds.), Nonlinear Differential Equations and Applications, Pitman, London (1985).

    Google Scholar 

  8. J. C. Lopez-Marcos and J. M. Sanz-Sema, Stability and convergence in numerical analysis III: linear investigation of nonlinear stability,SIAM J. Numer. Anal.,8, 71–84 (1988).

    MATH  Google Scholar 

  9. N. V. Ardelyan, A method of investigation of nonlinear difference schemes,Diff. Uravnenya,23, 1116–1126 (1987).

    MathSciNet  Google Scholar 

  10. J. M. Ortega and W. C. Reinboldt,Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, London (1970).

    MATH  Google Scholar 

  11. A. D. Liashko, On the correctness of two-layer operator-difference schemes,Dokl. Akad. Nauk SSSR,215, 1017–1021 (1974).

    Google Scholar 

  12. A. D. Liashko and E. M. Fedotov, Correctness of one class of conservative nonlinear operator-difference schemes,IzvVuzov. Matematika,10, 47–55 (1985).

    Google Scholar 

  13. J. L. Lions,Some Methods for Solving Nonlinear Boundary Problems [Russian translation], Mir, Moscow (1972).

    Google Scholar 

  14. R. Ciegis and M. Meilūnas, On the difference scheme for a nonlinear diffusion-reaction type problem,Lief. Mat. Rinkinys,33, 16–29 (1993).

    Google Scholar 

  15. Raim. Čiegis, Rem. Čiegis and M. Meilūnas, On the convergence in theL 2 norm of difference schemes for systems of parabolic partial differential equation§,Lief. Mat. Rinkinys,33, 269–279 (1993).

    Google Scholar 

  16. R. Čiegis, On the convergence in C norm of symmetric difference schemes for the nonlinear evoliution problems,Liet. Mat. Rinkinys,32, 187–205 (1992).

    Google Scholar 

  17. R. Ciegis, Investigation of difference schemes for a class of models of excitability,Comput. Maths, and Math. Phys. 32, 757–767 (1992).

    MathSciNet  Google Scholar 

  18. R. Ciegis, On the convergence in theC norm of difference scheme for one nonlinear diffusion-reaction problem,Diff. Uravnenya,28, 1261–1271 (1992).

    MathSciNet  MATH  Google Scholar 

  19. Y. Kuramoto and T. Tsuzuki, On the formation of dissipative structures in reaction-diffusion systems.Progr. Theor. Phys.,54, 687–699 (1975).

    Article  Google Scholar 

  20. G. Z. Tsertsvadze, On the convergence of difference schemes for the Kuramoto-Tsuzuki equation and systems of reaction-diffusion type,Comput. Maths, and Math. Phys.,31, 698–707 (1991).

    MathSciNet  MATH  Google Scholar 

  21. F. Ivanauskas, The convergence and the stability of difference schemes for the nonlinear Schrödinger equations, the Kuramoto-Tsuzuki equation and reaction-diffusion systems,Dokl. Akad. Nauk,337, 570–574 (1994).

    Google Scholar 

  22. G. I. Marchuk and V. I. Agoshkov,Introduction to Projective Difference Methods [in Russian], Nauka, Moscow (1981).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Informatics, Akademijos 4, 2600, Vilnius, Lithuania

    Raimondas Čiegis

  2. Kaunas Faculty of Humanity, Vilnius University, Muitinės Str. 8, 3000, Kaunas, Lithuania

    Remigijus Čiegis

  3. Vilnius Technical University, Saulètekio Str. 11, 2600, Vilnius, Lithuania

    Mečislavas Meilūnas

Authors
  1. Raimondas Čiegis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Remigijus Čiegis
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mečislavas Meilūnas
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Lietuvos Matematikos Rinkinys, Vol. 36, No. 3, pp. 281–302, July-September, 1996.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Čiegis, R., Čiegis, R. & Meilūnas, M. On a general method for investigation of finite difference schemes. Lith Math J 36, 224–240 (1996). https://doi.org/10.1007/BF02986849

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02986849

Keywords

Search

Navigation