Skip to main content
SpringerLink
Log in

Numerical methods of high-order accuracy for nonlinear boundary value problems

II. Nonlinear boundary conditions

  • 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. Browder, F. E.: Existence and uniqueness theorems for solutions of nonlinear boundary value problems. Proc. of Symp. in Applied Math. Vol. XVII, Applications of Nonlinear Partial Differential Equations in Mathematical Physics, American Mathematical Society, 24–29 (1965).

  2. Ciarlet, P. G.: Variational methods for non-linear boundary-value problems (103 pp.). Doctoral Thesis, Case Institute of Technology 1966.

  3. —M. H. Schultz, andR. S. Varga: Numerical methods of high-order accuracy for nonlinear two-point boundary value problems. Proceedings of the International Colloquium C. N. R. S., Besangon, France, Sept. 7–14, 1966 (to appear).

  4. — Numerical methods of high-order accuracy for nonlinear boundary value problems. I. One dimensional problem. Numer. Math.9, 394–430 (1967).

    Google Scholar 

  5. — Numerical methods of high-order accuracy for nonlinear boundary value problems. Monotone operators (to appear).

  6. Collatz, L.: The numerical treatment of differential equations, 3rd. ed. (568 pp.). Berlin-Göttingen-Heidelberg: Springer 1960.

    Google Scholar 

  7. Courant, R., andD. Hilbert: Methods of mathematical physics. Vol. 1 (561 pp.). New York: Interscience 1953.

    Google Scholar 

  8. Herbold, R. J.: Consistent quadrature schemes for the numerical solution of boundary value problems by variational techniques (189 pp.). Doctoral Thesis, Case Institute of Technology 1968.

  9. Keller, H. B.: Existence theory for two-point boundary problems. Bull. Amer. Math. Soc.72, 728–731 (1966).

    Google Scholar 

  10. Kellogg, R. B.: Personal communication.

  11. Lorentz, G. G.: Approximation of functions (188 pp.). New York: Holt, Rinehart, and Winston 1966.

    Google Scholar 

  12. Mikhlin, S. G.: Variational methods in mathematical physics (582 pp.). New York: Macmillan Co. 1964.

    Google Scholar 

  13. Schechter, S.: Iteration methods for nonlinear problems. Trans. Amer. Math. Soc.104, 179–189 (1962).

    Google Scholar 

  14. Schultz, M. H., andR. S. Varga:L-splines. Numer. Math.10, 345–369 (1967).

    Google Scholar 

  15. Yosida, K.: Functional analysis (458 pp.). New York: Academic Press 1965.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Case Western Reserve University, University Circle 10900 Euclid Avenue, 44106, Cleveland, Ohio, USA

    P. G. Ciarlet, M. H. Schultz &  R. S. Varga

Authors
  1. P. G. Ciarlet
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. H. Schultz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. S. Varga
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was supported in part by NSF Grant GP-5553.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ciarlet, P.G., Schultz, M.H. & Varga, R.S. Numerical methods of high-order accuracy for nonlinear boundary value problems. Numer. Math. 11, 331–345 (1968). https://doi.org/10.1007/BF02166686

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02166686

Keywords

Search

Navigation