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ONE PARAMETER FAMILY OF LINEAR DIFFERENCE EQUATIONS AND THE STABILITY PROBLEM FOR THE NUMERICAL SOLUTION OF ODEsL. ACETO, R. PANDOLFI, AND D. TRIGIANTE Received 21 July 2004; Accepted 4 October 2004The 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...
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ONE PARAMETER FAMILY OF LINEAR DIFFERENCE EQUATIONS AND THE STABILITY PROBLEM FOR THE NUMERICAL
