Some relationships Between Implicit Runge-Kutta, Collocation and Lanczos & Methods and their Stability Properties

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  2. Dr Kenneth Wright
Author(s)Wright K
Series Editor(s)Cox, NSM
Publication type Report
Series TitleComputing Laboratory Technical Report Series
Source Publication DateNovember 1969
Report Number2
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In this paper relationships between various one-step methods for the initial value problem in ordinary differential equations are discussed and a unified treatment of the stability properties of the methods is given. The analysis provides some new results on stability as well as alternative derivations for some known results. The term stability is used in the sense of A-Stability as introduced by Dahlquist. Conditions for any polynomial collocations method or its equivalent to be A-Stable are derived. These conditions may be easily checked in any particular case.
InstitutionComputing Laboratory, The University of Newcastle upon Tyne
Place PublishedNewcastle upon Tyne
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