Skip to main content
SpringerLink
Log in

A note on initial-value formulations of elliptic boundary-value problems

  • Brief Reports
  • Published:
Zeitschrift für angewandte Mathematik und Physik ZAMP Aims and scope Submit manuscript

Summary

An elliptic boundary-value problem may be formulated as an initial-value problem by approximating it as a two-point boundary-value problem. A method proposed in [6] not requiring this approximation is disproved by means of an example.

Zusammenfassung

Ein elliptisches Randwertproblem lässt sich als Anfangswerproblem, formulieren, indem es durch ein Zweipunkt-Randwertproblem approximiert wird. Eine in [6] vorgeschlagene Methode, die auf diese Approximation verzichtet, wird durchein Beispiel widerlegt.

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. R. Bellman, R. Kalaba, andG. M. Wing,Invariant Imbedding and the Reduction of Two-Point Boundary-Value Problems to Initial-Value Problems, Proc. Nat. Acad. Sci. USA46, 1646–1649 (1960).

    Google Scholar 

  2. E. Angel,Dynamic Programming and Linear Partial Equations, J. Math. Anal. Appl.23, 628–638 (1968).

    Google Scholar 

  3. E. Angel,Discrete Invariant Imbedding and Elliptic Boundary-Value Problems Over Irregular Regions, J. Math. Anal. Appl.23, 471–484 (1968).

    Google Scholar 

  4. E. Angel andA. Jain,Initial-Value Transformations for Elliptic Boundary Value Problems, J. Math. Anal. Appl.35, 496–502 (1971).

    Google Scholar 

  5. H. J. Brauchli,An Alternate Formulation of a Method of L. V. Kantorovich, UARI Research Rep. No. 91, AFOSR Scientific Report, Project Themis-AFOSR 70-2867TR., Research Institute, The University of Alabama in Huntsville, Huntsville, Alabama, October 1970.

    Google Scholar 

  6. C. W. Maynard andM. R. Scott,Invariant Imbedding of Linear Partial Differential Equations via Generalized Riccati Transformations, J. Math. Anal. Appl.36, 432–459 (1971).

    Google Scholar 

Download references

Author information

Author notes

  1. Hans J. Brauchli

    Present address: Fachgruppe für Mechanik, Swiss Federal Institute of Technology, Zürich

Authors and Affiliations

  1. The University of Alabama in Huntsville, Huntsville, Alabama, USA

    Hans J. Brauchli

Authors
  1. Hans J. Brauchli
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The author is thankful for support by the AFOSR, through contract No. F4462-69-C-0124 and NASA-UAH Agreement Modification 4.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Brauchli, H.J. A note on initial-value formulations of elliptic boundary-value problems. Journal of Applied Mathematics and Physics (ZAMP) 23, 991–993 (1972). https://doi.org/10.1007/BF01596226

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01596226

Keywords

Search

Navigation