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Numerische Mathematik

, Volume 44, Issue 2, pp 233–245 | Cite as

Numerical error bounds for fourth order boundary value problems, simultaneous estimation ofu(x) andu″(x)

  • Johann Schröder
Article

Summary

For certain nonlinear two-point boundary value problems of the fourth order an estimation theory is developed which yields simultaneous estimates of the solution and its second derivative. Methods for computing numerical error bounds for approximate solutions are described and tested. The theory provides also uniqueness and existence statements. The results can be applied to many problems for which a corresponding theory on two-sided bounds is not suitable.

Subject Classifications

AMS (MOS): 34A40, 34A50, 34B15, 65L16 CR5.11, 5.17 

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References

  1. 1.
    Ehlich, H., Zeller, K.: Schwankung von Polynomen zwischen Gitterpunkten. Math. Z.86, 41–44 (1964)Google Scholar
  2. 2.
    Ruttmann, B.: Untersuchungen zur Fehlerabschätzung von polynomialen Näherungslösungen bei Randwertaufgaben gewöhnlicher Differentialgleichungen. Diss. Univ. Köln, 1982Google Scholar
  3. 3.
    Schröder, J.: Operator Inequalities. New York: Academic Press 1980Google Scholar
  4. 4.
    Schröder, J.: Fourth order two-point boundary value problems; estimates by two-sided bounds. Nonlinear Analysis (in press)Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Johann Schröder
    • 1
  1. 1.Mathematisches InstitutUniversität KölnKöln 41(Fed. Rep.)

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