Stability Analysis of Linear Multistep Methods via Polynomial Type Variation

Date of Online Publication: 14/04/2007
Keywords: Linear multistep methods, Stability of numerical methods, polynomial type
Authors: L. Aceto, R. Pandolfi, D. Trigiante
Pages: 1-9
The linear stability analysis for linear multistep methods leads to study the location of the roots of the associated characteristic polynomial with respect to the unit circle in the complex plane. It is known that if the discrete problem is an initial value one, it is suficient to determine when all the roots are inside the unit disk. This requirement is, however, conicting with the order conditions, as established by the Dahlquist barrier. The conict disappears if one uses a linear multistep method coupled with boundary conditions (BVMs). In this paper, a rigorous analysis of the linear stability for some classes of BVMs is presented. The study is carried out by using the notion of type of a polynomial.


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