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  • Research Article
  • 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:

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.

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Functional Equation

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Authors’ Affiliations

(1)
Dipartimento di Matematica Applicata "U. Dini,", Università di Pisa, Via Diotisalvi 2, Pisa, 56126, Italy
(2)
Dipartimento di Matematica "U. Dini,", Università di Firenze, Viale Morgagni 67/A, Firenze, 50134, Italy
(3)
Dipartimento di Energetica "S. Stecco,", Università di Firenze, Via C. Lombroso 6/17, Firenze, 50134, Italy

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