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Some relationships between implicit Runge-Kutta, collocation and Lanczos tau methods and their stability properties

Lookup NU author(s): Dr Kenneth Wright

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Abstract

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 ofA-Stability as introduced by Dahlquist. Conditions for any polynomial collocation method or its equivalent to beA-Stable are derived. These conditions may be easily checked in any particular case.

Publication metadata

Author(s): Wright K

Publication type: Article

Publication status: Published

Journal: BIT

Year: 1970

Volume: 10

Issue: 2

Pages: 217-227

ISSN (print): 0006-3835

ISSN (electronic): 1572-9125

Publisher: Springer Netherlands

URL: http://dx.doi.org/10.1007/BF01936868

DOI: 10.1007/BF01936868

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