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One Class of Splitting Iterative Schemes

  • Čiegis Čiegis
  • V. Pakalnytė
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2330)

Abstract

This paper deals with the stability analysis of a new class of iterative methods for elliptic problems. These schemes are based on a general splitting method, which decomposes a multidimensional parabolic problem into a system of one dimensional implicit problems. We use a spectral stability analysis and investigate the convergence order of two iterative schemes. Finally, some results of numerical experiments are presented.

References

  1. 1.
    Abrashin, V.N.: On the stability of multicomponent additive direction method. Differentsialnyje uravnenyja. 35 (1999) 212–224 (in Russian).MathSciNetGoogle Scholar
  2. 2.
    Abrashin, V.N., Zhadaeva, N.G.: On the convergence rate of economical iterative methods for stationary problems of mathematical physics. Differentsialnyje uravnenyja. 36 (2000) 1422–1432 (in Russian).MathSciNetGoogle Scholar
  3. 3.
    Aleinikova, T., Čiegis, R.: Investigation of new iterative methods for solving multidimensional elliptic equations. Differentsialnyje uravnenyja. 29 (1993) 1124–1129 (in Russian).Google Scholar
  4. 4.
    Marchuk, G.I. Splitting methods. Nauka, Moscow, 1988. (in Russian).Google Scholar
  5. 5.
    Peaceman, D., Rachford, H.: The numerical solution of parabolic and elliptic differential equations. SIAM, 3 (1955).Google Scholar
  6. 6.
    Samarskii, A.A., Nikolajev, E.S. Methods for solving difference equations. Nauka, Moscow, 1978.(in Russian).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Čiegis Čiegis
    • 1
  • V. Pakalnytė
    • 1
  1. 1.Vilnius Gediminas Technical UniversityVilniusLithuania

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