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The method of the hypercircle for a class of nonlinear equations

Published online by Cambridge University Press:  17 February 2009

A. M. Arthurs  and
V. G. Hart
A. M. Arthurs
Affiliation:
Department of Mathematics, University of York, York, YO1 5DD, England
V. G. Hart
Affiliation:
Department of Mathematics, University of Queensland, St. Lucia, Q 4067, Australia
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Abstract

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We present a geometrical method for the solution of a certain class of non-linear boundary value problems. The results generalize those of the standard hypercircle method for linear problems. Two illustrative examples are described.

Type
Research Article
Information
The ANZIAM Journal , Volume 21 , Issue 1 , April 1979 , pp. 75 - 83
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Arthurs, A. M., Complementary variational principles (Oxford: Clarendon Press, 1970), Chapter 4.Google Scholar
[2]Arthurs, A. M., “Dual extremum principles and error bounds for a class of boundary value problems”, J. Math. Anal. Appl. 41 (1973), 781–795.Google Scholar
[3]Arthurs, A. M., “On variational principles and the hypercircie for boundary value problems”, Proc. Roy. Irish Acad. 77A (1977), 75–83.Google Scholar
[4]Bailey, P. B., Shampine, L. F. and Waltman, P. E., Nonlinear two-point boundary value problems (New York: Academic Press, 1968), p. 117Google Scholar
[5]Collatz, L., “Aufgaben monotoner Art”, Arch. Math. 3 (1952), 366–376.Google Scholar
[6]Noble, B. and Sewell, M. J., “On dual extremum principles in applied mathematics”, J. Inst. Maths, and Applics. 9 (1972), 124–193.Google Scholar
[7]Synge, J. L., The hypercircle in mathematical physics (Cambridge University Press, 1957).Google Scholar