Skip to main content
SpringerLink
Log in

A numerical method for the exterior Dirichlet problem for the reduced wave equation

  • 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. Brakhage, H., & P. Werner, Über das Dirichletsche Außenraumproblem für die Helmholtzsche Schwingungsgleichung. Archiv d. Math. 16, 325–329 (1965).

    Google Scholar 

  2. Bramble, J.H., Error estimates for difference methods in forced vibration problems. Tech. Note BN-388, Inst. Fluid Dyn. and Applied Math., U. Maryland, 1965.

  3. Eidus, D.M., On the principle of limiting absorption. Math. Sbornik 57, 13–44 (1962). English translation: New York University, Courant Institute of Mathematical Sciences, Research Report No. EM-191, 1963.

    Google Scholar 

  4. Freudenthal, H., Über ein Beugungsproblem aus der elektromagnetischen Lichttheorie. Compositio Math. 6, 221–227 (1938).

    Google Scholar 

  5. Greenspan, D., Introductory Numerical Analysis of Elliptic Boundary Value Problems. New York: Harper and Row 1965.

    Google Scholar 

  6. Greenspan, D., & E. Silverman, Approximate solution of the exterior Dirichlet problem and the calculation of electrostatic capacity. Technical Report No. 538, Mathematics Research Center, U. Wisconsin, 1965.

    Google Scholar 

  7. Hitchcock, A.J.M., Polynomial approximations to Bessel functions of order zero and one and to related functions. Mathematical Tables and Other Aids to Computation 11, 86–88 (1957).

    Google Scholar 

  8. Kantorovitch, L.V., & V.I. Krylov, Approximate Methods of Higher Analysis. New York: C.D. Benster, tr. Interscience 1958.

    Google Scholar 

  9. Keller, J.B., Geometrical theory of diffraction. Journal of the Optical Soc. of America 52, 116–130 (1962).

    Google Scholar 

  10. Kline, M., & I.W. Kay, Electromagnetic Theory and Geometrical Optics. New York: Interscience 1965.

    Google Scholar 

  11. Kussmaul, R., Diplomarbeit TH Karlsruhe, 1966.

  12. Kussmaul, R., & P. Werner, Fehlerabschätzungen für ein numerisches Verfahren zur Auflösung linearer Integralgleichungen mit schwachsingulären Kernen. (To appear.)

  13. Leis, R., Zur Dirichletschen Randwertaufgabe des Außenraumes der Schwingungsgleichung. Math. Zeitschr. 90, 205–211 (1965).

    Google Scholar 

  14. MacCamy, R.C., Low frequency acoustic oscillations. Quarterly Appl. Math. 23, 247–256 (1965).

    Google Scholar 

  15. Panič, O.J., On the solubility of exterior boundary value problems for the wave equation and for a system of Maxwell's equations [Russian]. Uspeshi Mat. Nauk 20, 221–226 (1965).

    Google Scholar 

  16. Rellich, F., Über das asymptotische Verhalten der Lösungen von Δu+λu=0 in unendlichen Gebieten. Jahresber. Deutsch. Math.-Verein. 53, 57–65 (1943).

    Google Scholar 

  17. Shenk, N., Spectral representations and scattering theory for the wave equation. Thesis, Stanford, 1965.

  18. Smirnow, W.I., Lehrgang der Höheren Mathematik, Teil III, 2. Berlin: Deutscher Verlag der Wissenschaften 1965.

    Google Scholar 

  19. Smirnow, W.L., Lehrgang der Höheren Mathematik, Teil IV. Berlin: Deutscher Verlag der Wissenschaften 1958.

    Google Scholar 

  20. Werner, P., Zur mathematischen Theorie akustischer Wellenfelder. Arch. Rational Mech. Anal. 6, 231–260 (1960).

    Google Scholar 

  21. Werner, P., Randwertprobleme der mathematischen Akustik. Arch. Rational Mech. Anal. 10, 29–66 (1962).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Research Center, United States Army University of Wisconsin, USA

    Donald Greenspan & Peter Werner

Authors
  1. Donald Greenspan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peter Werner
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by L. Collatz

The work reported here was sponsored by the Mathematics Research Center, United States Army, Madison, Wisconsin, under Contract No. DA-11-022-ORD-2059.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Greenspan, D., Werner, P. A numerical method for the exterior Dirichlet problem for the reduced wave equation. Arch. Rational Mech. Anal. 23, 288–316 (1966). https://doi.org/10.1007/BF00281165

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00281165

Keywords

Search

Navigation