Lithuanian Mathematical Journal

, Volume 37, Issue 2, pp 119–128 | Cite as

On extension of one method for investigation of nonlinear difference schemes

  • Raim Čiegis
  • Rem Čiegis
  • O. Štikonienė


Difference Scheme Maximum Norm Truncation Error Finite Difference Scheme Global Error 
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  1. 1.
    Raim. Čiegis, Rem. Čiegis, and M. Meilũnas On a general method for investigation of finite difference schemes,Lith. Math. J.,36, 224–241 (1996).CrossRefMATHGoogle Scholar
  2. 2.
    J. C. Lopez-Marcos and J. M. Sanz-Serna, Stability and convergence in numerical analysis III: linear investigation of nonlinear stability,IMA J. Numer. Anal.,8, 71–84 (1988).MATHMathSciNetGoogle Scholar
  3. 3.
    F. Ivanauskas, The convergence and the stability of difference schemes for the nonlinear Schrödinger equations, the Kuramoto-Tsuzuki equation, and reaction-diffusion systemsDokl. Akad. Nauk,337, 570–574 (1994).Google Scholar
  4. 4.
    A. M. Stuart and A. R. Humphries, Model problems in numerical stability theory for initial value problems,SIAM Review,36, 226–257 (1994).MATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    A. D. Liashko and E. M. Fedotov, Correctness of one class of conservative nonlinear operator-difference schemes,Izv. Vuzov, Matematika,10, 47–55 (1985).Google Scholar
  6. 6.
    J. M. Sanz-Serna Stability and convergence in numerical analysis I: Linear problems, a simple, comprehensive account, in:Nonlinear Differential Equations and Applications J. K. Hale and P. Martinez-Aneores (Eds.), Pitman, London (1985).Google Scholar
  7. 7.
    J. G. Heywood and R. Rannacher, Finite element approximation of the Navier-Stokes problem. Part II: Stability of solutions and error estimates uniform in time,SIAM J. Numer. Anal. 23, 750–777 (1986).MATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    R. Čiegis, On the convergence inC norm of symmetric difference schemes for the nonlinear evoliution problems,Liet. Matem. Rink.,32, 187–205 (1992).Google Scholar
  9. 9.
    S. Larsson, The long-time behavior of finite-element approximations of solutions to semilinear parabolic problems,SIAM J. Numer. Anal.,26, 348–365 (1989).MATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    R. Čiegis, The convergence analysis of finite difference schemes for diffusion-reaction problems,Habil. Dr. Thesis, Institute of Mathematics and Informatics, Vilnius, Lithuania (1993).Google Scholar
  11. 11.
    F. Rothe,Global Solutions of Reaction-Diffusion Systems, Lecture Notes in Mathematics 1072, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo (1984).MATHGoogle Scholar
  12. 12.
    Y. Kuramoto and T. Tsuzuki, On the formation of dissipative structures in reaction-diffusion systems,Progr. Theor. Phys.,54, 687–699 (1975).CrossRefGoogle Scholar
  13. 13.
    W. E. Schiesser,Computational Mathematics in Engineering and Applied Science, ODEs, DAEs, and PDEs, CRC Press, Boca Raton-Ann Arbor-London-Tokyo (1993).MATHGoogle Scholar
  14. 14.
    A. Friedman,Mathematics in Industrial Problems, Part 3, IMA Math. Appl., Vol. 31, Springer-Verlag, New York (1990).MATHGoogle Scholar
  15. 15.
    B. P. Sommeijer, P. J. van der Houwen, and J. Kok, Time integration of three dimensional numerical transport models, Report NM-R9316, Centre for Mathematics and Computer Science, Amsterdam (1993).Google Scholar
  16. 16.
    A. A. Samarskij,The Theory of Difference Schemes [in Russian], Nauka, Moscow (1988).MATHGoogle Scholar
  17. 17.
    F. Ivanauskas and T. Meškauskas, On convergence and stability of difference schemes for derivative nonlinear evolution equations,Liet. Matem. Rink.,36, 10–20 (1996).MATHGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • Raim Čiegis
    • 1
  • Rem Čiegis
    • 2
  • O. Štikonienė
    • 1
  1. 1.Institute of Mathematics and InformaticsVilniusLithuania
  2. 2.Kaunas Faculty of the HumanitiesVilnius UniversityKaunasLithuania

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