One parameter family of linear difference equations and the stability problem for the numerical solution of ODEs
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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.
KeywordsDifferential Equation Partial Differential Equation Ordinary Differential Equation Functional Analysis Functional Equation
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