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A note on stability
of the Douglas splitting method


Author: Willem Hundsdorfer
Journal: Math. Comp. 67 (1998), 183-190
MSC (1991): Primary 65M06, 65M12, 65M20
DOI: https://doi.org/10.1090/S0025-5718-98-00914-4
MathSciNet review: 1443119
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Abstract | References | Similar Articles | Additional Information

Abstract: In this note some stability results are derived for the Douglas splitting method. The relevance of the theoretical results is tested for an advection-reaction equation.


References [Enhancements On Off] (What's this?)

  • 1. J. Douglas, Alternating direction method for three space variables. Numer. Math. 4, pp. 41-63 (1962). MR 24:B2122
  • 2. J. Douglas, J.E. Gunn, A general formulation of alternating direction methods. Numer. Math. 6, pp. 428-453 (1964). MR 31:894
  • 3. W. Hundsdorfer, Trapezoidal and midpoint splittings for initial-boundary value problems. CWI Report, 1996.
  • 4. G.I. Marchuk, Splitting and alternating direction methods. Handbook of Numerical Analysis 1 (P.G. Ciarlet. J.L. Lions, eds.), North-Holland, Amsterdam, pp. 197-462, 1990. CMP 90:08
  • 5. A.R. Mitchell, D.F. Griffiths, The Finite Difference Method in Partial Differential Equations. John Wiley & Sons, Chichester, 1980. MR 82a:65002
  • 6. R.F. Warming, R.M. Beam, An extension of $A$-stability to alternating direction methods. BIT 19, pp. 395-417 (1979). MR 80h:65072

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Additional Information

Willem Hundsdorfer
Affiliation: CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands

DOI: https://doi.org/10.1090/S0025-5718-98-00914-4
Keywords: Numerical analysis, initial-boundary value problems, splitting methods
Received by editor(s): July 29, 1996
Article copyright: © Copyright 1998 American Mathematical Society

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