BIT Numerical Mathematics

, Volume 10, Issue 2, pp 217–227 | Cite as

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

  • K. 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 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.


Differential Equation Ordinary Differential Equation Computational Mathematic Stability Property Collocation Method 
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Copyright information

© BIT Foundations 1970

Authors and Affiliations

  • K. Wright
    • 1
  1. 1.Computing LaboratoryUniversity of Newcastle Upon TyneEngland

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