On the Abel Equation of the Second Kind with Sinusoidal Forcing
Articles
G. Alobaidi
American University of Sharjah, United Arab Emirates
R. Mallier
University of Western Ontario, Canada
Published 2007-01-25
https://doi.org/10.15388/NA.2007.12.1.14720
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Keywords

Abel equation
series solution
resonances
boundary layer

How to Cite

Alobaidi G. and Mallier R. (2007) “On the Abel Equation of the Second Kind with Sinusoidal Forcing”, Nonlinear Analysis: Modelling and Control, 12(1), pp. 33-44. doi: 10.15388/NA.2007.12.1.14720.

Abstract

We consider the Abel equation of the second kind with sinusoidal forcing, which is a model equation for western boundary outflow in the Stommel model of the large scale ocean circulation. Series solutions of this equation indicate the presence of resonances at certain discrete values of a parameter which measures the nonlinearity of the flow, but numerical solutions using a standard scheme show no evidence of these resonances. We discuss and resolve this apparent contradiction.

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