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Asymptotology—a cautionary tale

Published online by Cambridge University Press:  17 February 2009

R. L. Dewar
R. L. Dewar
Affiliation:
Department of Theoretical Physics and Plasma Research Laboratory, Research School of Physical Sciences and Engineering, Institute of Advanced Studies, The Australian National University, Canberra, ACT 0200, Australia; e-mail: robert.dewar@anu.edu.au.
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Abstract

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The art of asymptotology is a powerful tool in applied mathematics and theoretical physics, but can lead to erroneous conclusions if misapplied. A seemingly paradoxical case is presented in which a local analysis of an exactly solvable problem appears to find solutions to an eigenvalue problem over a continuous range of the eigenvalue, whereas the spectrum is known to be discrete. The resolution of the paradox involves the Stokes phenomenon. The example illustrates two of Kruskal's Principles of Asymptotology.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 44 , Issue 1 , July 2002 , pp. 33 - 40
Copyright
Copyright © Australian Mathematical Society 2002

References

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