Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-26T13:46:27.530Z Has data issue: false hasContentIssue false

Complementary variational principles for φiv = f(φ)

Published online by Cambridge University Press:  24 October 2008

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

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
Copyright
Copyright © Cambridge Philosophical Society 1970

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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(1)Noble, B. University of Wisconsin Mathematics Research Center Report No. 473 (1964, unpublished).Google Scholar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), 174184.CrossRefGoogle Scholar
(3)Arthurs, A. M.Proc. Cambridge Philos. Soc. 65 (1969), 803806.CrossRefGoogle Scholar
(4)Levinson, N.J.J. Math. Mech. 12 (1963), 567575.Google Scholar
(5)Mikhlin, S. G. In Differential equations and their applications (ed. Babuska, I.), Academic Press, New York (1963), 7792.Google Scholar
(6)Ciarlet, P. G., Schultz, M. H. and Varga, R. S.Numer. Math. 9 (1967), 394430.CrossRefGoogle Scholar
(7)Ciarlet, P. G., Schultz, M. H. and Varga, R. S.Numer. Math. 12 (1968), 266279.CrossRefGoogle Scholar