A note on stability of the Douglas splitting method
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- by Willem Hundsdorfer PDF
- Math. Comp. 67 (1998), 183-190 Request permission
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
- Jim Douglas Jr., Alternating direction methods for three space variables, Numer. Math. 4 (1962), 41–63. MR 136083, DOI 10.1007/BF01386295
- 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 176622, DOI 10.1007/BF01386093
- W. Hundsdorfer, Trapezoidal and midpoint splittings for initial-boundary value problems. CWI Report, 1996.
- 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.
- Andrew Ronald Mitchell and D. F. Griffiths, The finite difference method in partial differential equations, A Wiley-Interscience Publication, John Wiley & Sons, Ltd., Chichester, 1980. MR 562915
- 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, DOI 10.1007/BF01930993
Additional Information
- Willem Hundsdorfer
- Affiliation: CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands
- Received by editor(s): July 29, 1996
- © Copyright 1998 American Mathematical Society
- 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