Advances in Difference Equations

, 2006:019276 | Cite as

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

  • L Aceto
  • R Pandolfi
  • D Trigiante
Open Access
Research Article


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 ∈ ℂ-. 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.


Differential Equation Partial Differential Equation Ordinary Differential Equation Functional Analysis Functional Equation 
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Copyright information

© 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.

Authors and Affiliations

  1. 1.Dipartimento di Matematica Applicata "U. Dini,"Università di PisaPisaItaly
  2. 2.Dipartimento di Matematica "U. Dini,"Università di FirenzeFirenzeItaly
  3. 3.Dipartimento di Energetica "S. Stecco,"Università di FirenzeFirenzeItaly

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