Skip to main content
SpringerLink
Log in

A difference-analytical method for the computation of eigenvalues of the fourth-order equations with separated boundary conditions

  • Published:
Russian Mathematics Aims and scope Submit manuscript

Abstract

We propose a method for the computation of eigenvalues with odd multiplicities for spectral boundary-value problems of the 4th order with separated boundary conditions. In this method approximate eigenvalues appear as zeros of a certain function f(λ) which admits an explicit representation.

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. B. P. Demidovich, Lectures on the Mathematical Theory of Stability (Nauka, Moscow, 1967) [in Russian].

    Google Scholar 

  2. L.D. Akulenkoand S. V. Nesterov, “A Frequency-Parametric Analysis of Natural Oscillations of Non-Uniform Rods,” Prikl. Mat. Mekh. 67(4), 588–602 (2003).

    MathSciNet  Google Scholar 

  3. A. M. Akhtyamov, “Diagnosing the Fastening of a Ring Plate from its Vibration Eigenfrequencies,” Mekhan. Tverdogo Tela, No. 6, 137–147 (2003).

Download references

Author information

Authors and Affiliations

  1. Ufa Oil Technical State University, ul. Kosmonavtov 1, Ufa, 450062, Russia

    R. R. Abzalimov

  2. Ufa Aviation Technical State University, ul. K. Marksa 14, Ufa, 450000, Russia

    E. V. Salyakhova

Authors
  1. R. R. Abzalimov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. V. Salyakhova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. R. Abzalimov.

Additional information

Original Russian Text © R.R. Abzalimov and E.V. Salyakhova, 2008, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, No. 11, pp. 3–11.

About this article

Cite this article

Abzalimov, R.R., Salyakhova, E.V. A difference-analytical method for the computation of eigenvalues of the fourth-order equations with separated boundary conditions. Russ Math. 52, 1–9 (2008). https://doi.org/10.3103/S1066369X08110017

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X08110017

Key words

Search

Navigation