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

Numerische Mathematik volume 44, pages 233–245 (1984)Cite this 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.

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References

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Authors and Affiliations

  1. Mathematisches Institut, Universität Köln, D-5000, Köln 41, (Fed. Rep.)

    Johann Schröder

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  1. Johann Schröder
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Schröder, J. Numerical error bounds for fourth order boundary value problems, simultaneous estimation ofu(x) andu″(x) . Numer. Math. 44, 233–245 (1984). https://doi.org/10.1007/BF01410108

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  • DOI: https://doi.org/10.1007/BF01410108

Subject Classifications

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