Open Access

One parameter family of linear difference equations and the stability problem for the numerical solution of ODEs

Advances in Difference Equations20062006:019276

https://doi.org/10.1155/ADE/2006/19276

Received: 21 July 2004

Accepted: 4 October 2004

Published: 18 January 2006

Abstract

The study of the stability properties of numerical methods leads to considering linear difference equations depending on a complex parameter q. Essentially, the associated characteristic polynomial must have constant type for q -. Usually such request is proved with the help of computers. In this paper, by using the fact that the associated polynomials are solutions of a "Legendre-type" difference equation, a complete analysis is carried out for the class of linear multistep methods having the highest possible order.

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Authors’ Affiliations

(1)
Dipartimento di Matematica Applicata "U. Dini,", Università di Pisa
(2)
Dipartimento di Matematica "U. Dini,", Università di Firenze
(3)
Dipartimento di Energetica "S. Stecco,", Università di Firenze

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Copyright

© Hindawi Publishing Corporation 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.