Skip to main content
SpringerLink
Log in

Increasing efficiency of alternating triangular method based on improved spectral estimates

  • Published:
Mathematical Models and Computer Simulations Aims and scope

Abstract

A modified alternating triangular method is constructed for three-dimensional difference elliptic equations with the linear source function. Under the special restriction on the source function, the method requires \(n_0 (\varepsilon ) \cong O\left( {{1 \mathord{\left/ {\vphantom {1 {\sqrt[4]{{\left\| h \right\|}}}}} \right. \kern-\nulldelimiterspace} {\sqrt[4]{{\left\| h \right\|}}}}} \right)\) iterations. The improved estimate of the parameter is obtained for the alternating triangular method after the diagonal component of the matrix of the problem is considered separately, which helped reduce the number of iterations twice asymptotically. The improved spectral estimates and results of numerical experiments for the Dirichlet problem of the Poisson equation with the linear source function of the form q(x)u(x) and nonstationary heat conduction equation are given.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. N. Konovalov, “Optimal Adaptive Preconditioners in Static Problems of the Linear Theory of Elasticity,” Diff. Eq. 45, p. 1044 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  2. A. B. Kucherov and E. S. Nikolaev, “A Transverse Triangular Iterative Method for Solving Mesh Elliptic Equations in a Rectangle,” Zh. Vychisl. Mat. Mat. Fiz. 16(5), 1164–1174 (1976).

    Google Scholar 

  3. A. I. Sukhinov, “Modified Alternating Triangle Method for Heat Conduction and Filtration Problems,” in Computational Systems and Algorithms, (Izd-vo RGU, Rostov-on-Don, 1984), pp. 52–57.

    Google Scholar 

  4. A. A. Samarskii and P. N. Vabishchevich, Numerical Methods for Solving Convection-Diffusion Problems (Editorial URSS, Moscow, 2004) [in Russian].

    Google Scholar 

  5. A. A. Samarskii and E. S. Nikolaev, Numerical Methods for Grid Equations (Nauka, Moscow, 1978; Bikhauser Verlag, Basel, 1989).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Technology, Southern Federal University, GSP-17A, Nekrasovskii per. 44, Taganrog, 347928, Russia

    A. I. Sukhinov & A. V. Shishenya

Authors
  1. A. I. Sukhinov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. V. Shishenya
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. I. Sukhinov.

Additional information

Original Russian Text © A.I. Sukhinov, A.V. Shishenya, 2012, published in Matematicheskoe Modelirovanie, 2012, Vol. 24, No. 11, pp. 20–32.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sukhinov, A.I., Shishenya, A.V. Increasing efficiency of alternating triangular method based on improved spectral estimates. Math Models Comput Simul 5, 257–265 (2013). https://doi.org/10.1134/S2070048213030101

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S2070048213030101

Keywords

Search

Navigation