Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



An extension of the Kantorovich method

Author: Arnold D. Kerr
Journal: Quart. Appl. Math. 26 (1968), 219-229
DOI: https://doi.org/10.1090/qam/99857
MathSciNet review: QAM99857
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Abstract | References | Additional Information

Abstract: An extension of the Kantorovich method is discussed. The suggested method is demonstrated on the torsion problem of a beam of rectangular cross section. It is found that even when the solution is restricted to a one-term approximation, the method generates very good results also for stresses which are obtained as derivatives of the solution. It is shown that the final form of the generated solution is unique and that the convergence of the iterative process is very rapid. The obtained results indicate that the proposed method is a convenient tool to generate close approximate solutions, thus eliminating the arbitrariness in the choice of coordinate functions, which is a serious shortcoming inherent in the Ritz and Galerkin methods.

References [Enhancements On Off] (What's this?)

  • [1] L. V. Kantorovich and V. I. Krylov, Approximate methods of higher analysis, Translated from the 3rd Russian edition by C. D. Benster, Interscience Publishers, Inc., New York; P. Noordhoff Ltd., Groningen, 1958. MR 0106537
  • [2] L. V. Kantorovich, A direct method of solving the problem of the minimum of a double integral(in Russian) Izvestia AN, USSR, 1933, p. 647-652
  • [3] T. E. Schunck, Zur Knickfestigkeit schwach gekrümmter zylindrischer Schalen, Ingenieur Archiv, IV, 394-414 (1933)
  • [4] S. Timoshenko and J. N. Goodier, Theory of Elasticity, McGraw-Hill Book Company, Inc., New York, Toronto, London, 1951. 2d ed. MR 0045547

Additional Information

DOI: https://doi.org/10.1090/qam/99857
Article copyright: © Copyright 1968 American Mathematical Society

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