Numerics-characteristics-asymptotics: a case study from large scale ocean circulation

Authors: Hodnett, P. F.¹; Courtney, C.¹

Source: International Journal of Mathematical Education in Science and Technology, Volume 38, Number 8, January 2007 , pp. 1029-1049(21)

Publisher: Taylor and Francis Ltd

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Abstract:

This paper uses a partial differential equation which occurs in a reduced model of large scale circulation in an ocean basin as an educational vehicle through which to demonstrate the usefulness of a set of mathematical techniques in analysing the equation. A parameter occurring in the equation does in reality vary from very small through intermediate to very large values. Therefore separate solutions are required for (a) very small, (b) very large and (c) intermediate values of the parameter. This allows for the demonstration of how when the parameter is very small the method of characteristics and the singular perturbation method are useful. When the parameter is very large the regular perturbation method is useful. At intermediate values of the parameter numerical methods must be used and in this case it is a helpful check to have available the asymptotic results for both small and large values of the parameter.

Document Type: Research article

DOI: 10.1080/00207390601002864

Affiliations: 1: University of Limerick, Limerick, Republic of Ireland

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