Numerische Mathematik

, Volume 44, Issue 2, pp 247–259 | Cite as

Contractivity of locally one-dimensional splitting methods

  • J. G. Verwer


The aim of this paper is to study contractivity properties of two locally one-dimensional splitting methods for non-linear, multi-space dimensional parabolic partial differential equations. The term contractivity means that perturbations shall not propagate in the course of the time integration process. By relating the locally one-dimensional methods with contractive integration formulas for ordinary differential systems it can be shown that the splitting methods define contractive numerical solutions for a large class of non-linear parabolic problems without restrictions on the size of the time step.

Subject Classifications

AMS (MOS): 65L05 65M05 65M20 CR: 5.17 


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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • J. G. Verwer
    • 1
  1. 1.Mathematical CentreAmsterdamThe Netherlands

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