Skip to main content
SpringerLink
Log in

Numerical methods and existence theorems for ordinary differential equations

  • Published:
Numerische Mathematik 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. Dahlquist, Germund: Convergence and stability in the numerical integration of ordinary differential equations. Math. Scand.4, 33–53 (1956).—Stability and error bounds in the numerical integration of ordinary differential equations. Diss. Stockholm 1958.

    Google Scholar 

  2. Ince, E. L.: Ordinary differential equations, Sect. 3/4. London: Longmans, Green & Co., 1927 and New York: Dover Publications.

    Google Scholar 

  3. John, F.: On the integration of parabolic equations by difference methods. Communications Pure and Appl. Math.5, 155–211 (1952).

    Google Scholar 

  4. Lipschitz, R.: Sur la possibilité d'intégrer complètement un système donné d'équations différentielles. Bull. Sci. Math.10, 149–159 (1876).

    Google Scholar 

  5. Moigno, F. N. M.: Leçons de calcul, 2, p., 385 and 513. Paris: Gauthier-Villars 1844.

    Google Scholar 

  6. Osgood, W. F.: Beweise der Existenz einer Lösung der Differentialgleichungdy/dx=f(x, y) ohne Hinzunahme der Cauchy-Lipschitz-Bedingung. Mh. Math u. Physik9, 331–345 (1898).

    Google Scholar 

  7. Peano, G.: Démonstration de l'intégrabilité des équations differentielles ordinaires. Math. Ann.37, 182–228 (1890).

    Google Scholar 

  8. Richtmyer, R. D.: Difference methods for initial value problems, Chapt. 3. New York: Interscience Publishers, Inc.

Download references

Author information

Authors and Affiliations

  1. University of British Columbia, Vancouver, Canada

    T. E. Hull & W. A. J. Luxemburg

  2. California Institute of Technology, Pasadena 4, USA

    T. E. Hull & W. A. J. Luxemburg

Authors
  1. T. E. Hull
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. W. A. J. Luxemburg
    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

Hull, T.E., Luxemburg, W.A.J. Numerical methods and existence theorems for ordinary differential equations. Numer. Math. 2, 30–41 (1960). https://doi.org/10.1007/BF01386206

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01386206

Keywords

Search

Navigation