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Complementary variational principles for φiv = f(φ)

Published online by Cambridge University Press:  24 October 2008

N. Anderson  and
A. M. Arthurs
N. Anderson
Affiliation:
University of York
A. M. Arthurs
Affiliation:
University of York
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Abstract

Complementary variational principles are developed for boundary-value problems with field equations φiv = f(φ) in (0, 1) subject to φ(0) = φ(1) = 0, φ′(0) = φ′(1) = 0. The theory is applied in the non-linear case f(φ) = – keφ and accurate variational solutions, which are simple polynomials in x, are obtained.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 1 , July 1970 , pp. 173 - 177
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

(1)Noble, B. University of Wisconsin Mathematics Research Center Report No. 473 (1964, unpublished).Google Scholar
(2)Rall, L. B.J. Math. Anal. Appl. 14 (1966), 174–184.CrossRefGoogle Scholar
(3)Arthurs, A. M.Proc. Cambridge Philos. Soc. 65 (1969), 803–806.CrossRefGoogle Scholar
(4)Levinson, N.J.J. Math. Mech. 12 (1963), 567–575.Google Scholar
(5)Mikhlin, S. G. In Differential equations and their applications (ed. Babuska, I.), Academic Press, New York (1963), 77–92.Google Scholar
(6)Ciarlet, P. G., Schultz, M. H. and Varga, R. S.Numer. Math. 9 (1967), 394–430.CrossRefGoogle Scholar
(7)Ciarlet, P. G., Schultz, M. H. and Varga, R. S.Numer. Math. 12 (1968), 266–279.CrossRefGoogle Scholar