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

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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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Correspondence to L Aceto.

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Keywords

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