Skip to main content
SpringerLink
Log in

Linear self-adjoint multipoint boundary value problems and related approximation schemes

  • Published:
Numerische Mathematik Aims and scope Submit manuscript

Summary

Linear self-adjoint multipoint boundary value problems are investigated. The case of the homogeneous equation is shown to lead to spline solutions, which are then utilized to construct a Green's function for the case of homogeneous boundary conditions. An approximation scheme is described in terms of the eigen-functions of the inverse of the Green's operator and is shown to be optimal in the sense of then-widths of Kolmogorov. Convergence rates are given and generalizations to more general boundary value problems are discussed.

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. Agmon, S.: Lectures on elliptic boundary value problems. Princeton: Van Nostrand 1965.

    Google Scholar 

  2. Babuska, I., Prager, M., Vitasek, E.: Numerical processes in differential processes in differential equations. London: Interscience, Wiley 1966.

    Google Scholar 

  3. Golomb, M., Jerome, J.: Ordinary differential equations with boundary conditions on arbitrary point sets (to appear), TAMS.

  4. Grisvard, P.: Characterisation de quelques espaces d'interpolation. Arch. Rat. Mech. Anal.25, 40–63 (1967).

    Google Scholar 

  5. Halperin, I.: Introduction to the theory of distributions. Toronto: University of Toronto Press 1952.

    Google Scholar 

  6. Jerome, J.: On the ℒ2 n-width of certain classes of functions of several variables. J. Math. Anal. Appl.20, 110–123 (1967)

    Google Scholar 

  7. —— Onn-widths in Sobolev spaces and applications to elliptic boundary value problems. J. Math. Anal. Appl.29, 201–215 (1970).

    Google Scholar 

  8. ——, Schumaker, L.: OnLg splines. J. Approx. Th.2, 29–49 (1969).

    Google Scholar 

  9. Lorentz, G.: Approximation of functions. New York: Holt 1966.

    Google Scholar 

  10. Riesz, F., Sz.-Nagy, B.: Functional analysis. New York: Ungar 1955

    Google Scholar 

  11. Zettl, A.: Adjoint and self-Adoint boundary value problems with interface conditions. M.R.C. Technical Summary Report 827, Madison, Wisconsin, 1967.

    Google Scholar 

Download references

Author information

Author notes

  1. Joseph W. Jerome

    Present address: Department of Mathematics, Northwestern University, 60201, Evanston, Illinois, USA

Authors and Affiliations

    Authors
    1. Joseph W. Jerome
      View author publications

      You can also search for this author in PubMed Google Scholar

    Rights and permissions

    Reprints and permissions

    About this article

    Cite this article

    Jerome, J.W. Linear self-adjoint multipoint boundary value problems and related approximation schemes. Numer. Math. 15, 433–449 (1970). https://doi.org/10.1007/BF02165513

    Download citation

    • Received:

    • Issue Date:

    • DOI: https://doi.org/10.1007/BF02165513

    Keywords

    Search

    Navigation