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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
MathSciNet review: 1443119
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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. Jim Douglas Jr., Alternating direction methods for three space variables, Numer. Math. 4 (1962), 41–63. MR 0136083
  • 2. Jim Douglas Jr. and James E. Gunn, A general formulation of alternating direction methods. I. Parabolic and hyperbolic problems, Numer. Math. 6 (1964), 428–453. MR 0176622
  • 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. Andrew Ronald Mitchell and D. F. Griffiths, The finite difference method in partial differential equations, John Wiley & Sons, Ltd., Chichester, 1980. A Wiley-Interscience Publication. MR 562915
  • 6. R. F. Warming and Richard M. Beam, An extension of 𝐴-stability to alternating direction implicit methods, BIT 19 (1979), no. 3, 395–417. MR 548619, 10.1007/BF01930993

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Additional Information

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

Keywords: Numerical analysis, initial-boundary value problems, splitting methods
Received by editor(s): July 29, 1996
Article copyright: © Copyright 1998 American Mathematical Society