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Superharmonic solutions of nonlinear differential equations

McGuinness, Colm (1991) Superharmonic solutions of nonlinear differential equations. PhD thesis, Dublin City University.

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Abstract

This thesis is a study of the structure of superhaxmonic solutions of order m, to the sloshing equation introduced by Chester and Ockendon &; Ockendon, and to a lesser extent, Duffing’s equation. We use the Lyapunov Schmidt procedure to reduce these problems to two bifurcation equations. We elucidate the form and leading terms of the bifurcation equations. The usual scaling techniques fail when superharmonics of order 4 or greater are sought. An alternative scaling method is provided, which works for superharmonic solutions of all orders. The method is rigorous, and naturally provides an explicit approximation to the bifurcation surface. To produce a formula for the approximate bifurcation surface it is necessary to explicitly calculate coefficients in the bifurcation equations. A simple algorithm, which calculates the terms which may be required, is given. The method is implemented using Macsyma. The program, TAYLOR, produces the information for superharmonic and subharmonic solutions for a large class of nonlinear oscillation problems.

Item Type:Thesis (PhD)
Date of Award:1991
Refereed:No
Supervisor(s):Reynolds, David W.
Uncontrolled Keywords:Differential equations; Equations Numerical solutions
Subjects:Mathematics
DCU Faculties and Centres:DCU Faculties and Schools > Faculty of Science and Health > School of Mathematical Sciences
Use License:This item is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 3.0 License. View License
ID Code:19048
Deposited On:28 Aug 2013 14:58 by Celine Campbell . Last Modified 09 Oct 2013 14:56

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