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

Lookup NU author(s): Dr Kenneth Wright



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.

Publication metadata

Author(s): Wright K

Series Editor(s): Cox, NSM

Publication type: Report

Series Title: Computing Laboratory Technical Report Series

Year: 1969

Pages: [30]

Source Publication Date: November 1969

Report Number: 2

Institution: Computing Laboratory, The University of Newcastle upon Tyne

Place Published: Newcastle upon Tyne