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

Advances in Difference Equations volume 2006, Article number: 019276 (2006) Cite this article

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 ∈ 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.

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Authors and Affiliations

  1. Dipartimento di Matematica Applicata "U. Dini,", Università di Pisa, Via Diotisalvi 2, Pisa, 56126, Italy

    L Aceto

  2. Dipartimento di Matematica "U. Dini,", Università di Firenze, Viale Morgagni 67/A, Firenze, 50134, Italy

    R Pandolfi

  3. Dipartimento di Energetica "S. Stecco,", Università di Firenze, Via C. Lombroso 6/17, Firenze, 50134, Italy

    D Trigiante

Authors
  1. L Aceto
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  2. R Pandolfi
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  3. D Trigiante
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Corresponding author

Correspondence to L Aceto.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Aceto, L., Pandolfi, R. & Trigiante, D. One parameter family of linear difference equations and the stability problem for the numerical solution of ODEs. Adv Differ Equ 2006, 019276 (2006). https://doi.org/10.1155/ADE/2006/19276

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

Keywords

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