Open Access

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

Advances in Difference Equations20062006:019276

DOI: 10.1155/ADE/2006/19276

Received: 21 July 2004

Accepted: 4 October 2004

Published: 18 January 2006


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.


Authors’ Affiliations

Dipartimento di Matematica Applicata "U. Dini,", Università di Pisa
Dipartimento di Matematica "U. Dini,", Università di Firenze
Dipartimento di Energetica "S. Stecco,", Università di Firenze


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© Hindawi Publishing Corporation 2006

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