BIT Numerical Mathematics

, Volume 29, Issue 2, pp 328–346 | Cite as

Remarks on Picard-Lindelöf iteration

Part I
  • Olavi Nevanlinna
Part II Numerical Mathematics
Received:
Revised:

Abstract

The paper discusses Picard-Lindelöf iteration for systems of autonomous linear equations on finite intervals, as well as its numerical variants. Most of the discussion is under a model assumption which roughly says that the coupling terms are of moderate size compared with the slow time scales in the problem. It is shown that the speed of convergence is quite independent of the step sizes already for very large time steps. This makes it possible to design strategies in which the mesh gets gradually refined during the iteration in such a way that the iteration error stays essentially on the level of discretization error.

Subject classifications AMS

65L05 65F10 

Keywords

Picard-Lindelöf iteration waveform relaxation weak coupling 
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Copyright information

© BIT Foundations 1989

Authors and Affiliations

  • Olavi Nevanlinna
    • 1
  1. 1.Institute of MathematicsHelsinki University of TechnologyEspooFinland

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