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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)
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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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
- Differential Equation
- Partial Differential Equation
- Ordinary Differential Equation
- Functional Analysis
- Functional Equation