Skip to main content
SpringerLink
Log in

Bounds for eigenvalues of the Sturm-Liouville problem by finite difference methods

  • Published:
Archive for Rational Mechanics and Analysis 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

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Bückner, H.: Über Konvergenzsätze, die sich bei der Anwendung eines Differenzverfahrens auf ein Stúrm-Liouvillesches Eigenwertproblem ergeben. Math. Z. 51, 423–465 (1946).

    Google Scholar 

  2. Collatz, L.: The Numerical Treatment of Differential Equations, 3rd Edition. Berlin-Göttingen-Heidelberg: Springer 1960.

    Google Scholar 

  3. Collatz, L.: Konvergenzbeweis und Fehlerabschätzung für das Differenzverfahren bei Eigenwertproblemen gewöhnlicher Differentialgleichungen zweiter und vierter Ordnung. Deutsche Math. 2, 189–215 (1937).

    Google Scholar 

  4. Courant, R.: Variational methods for the solutions of problems of equilibrium and vibrations. Bull. Amer. Math. Soc. 49, 1–23 (1943).

    Google Scholar 

  5. Courant, R., & D. Hilbert: Methods of Mathematical Physics, Vol. I, first English edition. New York: Interscience 1953.

    Google Scholar 

  6. Courant, R., & D. Hilbert: Methoden der Mathematischen Physik, Vol. II, first edition. Berlin: Springer 1937.

    Google Scholar 

  7. Farrington, C. C., R. T. Gregory & A. H. Taub: On the numerical solution of Sturm-Liouville differential equation. M. T. A. C. 11, 131–150 (1957).

    Google Scholar 

  8. Fox, L.: The Numerical Solution of Two-Point Boundary Problems in Ordinary Differential Equations, 1st edition. Oxford: Clarendon Press 1957.

    Google Scholar 

  9. Hersch, J.: Équations différentielles et fonctions des cellules. C. R. Acad. Sci. Paris 240, 1602–1604 (1955).

  10. Hubbard, B.: Bounds for eigenvalues of the free and fixed membrane by finite difference methods. Pacific J. Math. (to appear).

  11. Hubbard, B.: Eigenvalues of the non-homogeneous rectangular membrane by finite difference methods. Arch. Rational Mech. Anal. 9, 121–133 (1962).

    Google Scholar 

  12. Poincaré, H.: Sur les équations aux dérivées partielles de la physique mathématique. Amer. J. of Math. 12, 211–294 (1890).

    Google Scholar 

  13. Treuenfels, P.: Remark on a paper of L. Collatz on bounds for eigenvalues of differential equations. Notices A. M. S. 7, 358 (1960).

    Google Scholar 

  14. Weinberger, H. F.: Upper and lower bounds for eigenvalues by finite difference methods. Comm. Pure Appl. Math. 9, 613–623 (1956).

    Google Scholar 

  15. Weinberger, H. F.: Lower bounds for higher eigenvalues by finite difference methods. Pacific J. Math. 8, 339–368 (1958).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Fluid Dynamics and Applied Mathematics University of Maryland, College Park, Maryland, USA

    B. E. Hubbard

Authors
  1. B. E. Hubbard
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by L. Collatz

This research was supported in part by the United States Air Force Office through the Air Force Office of Scientific Research of the Air Research and Development Command under Contract No. AF 49(638)228 and in part by the foundational research program of the U. S. Naval Ordnance Laboratory, Task Number FR-30.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hubbard, B.E. Bounds for eigenvalues of the Sturm-Liouville problem by finite difference methods. Arch. Rational Mech. Anal. 10, 171–179 (1962). https://doi.org/10.1007/BF00281184

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00281184

Keywords

Search

Navigation