The Equivalence of Certain Alternating Direction and Locally One-Dimensional Difference Methods

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Previous article Next article The Equivalence of Certain Alternating Direction and Locally One-Dimensional Difference MethodsA. R. Gourlay and Andrew R. MitchellA. R. Gourlay and Andrew R. Mitchellhttps://doi.org/10.1137/0706004PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] F. G. D'yakonov, On some difference schemes for solutions of boundary problems, U.S.S.R Comput. Math. and Math. Phys., 2 (1962), 55–77 10.1016/0041-5553(63)90270-2 0233.65052 CrossrefGoogle Scholar[2] G. Fairweather and , A. R. Mitchell, Some computational results of a new alternating direction procedure, Comput. J., 9 (1966), 298–303 CrossrefISIGoogle Scholar[3] G. Fairweather and , A. R. Mitchell, A new computational procedure for ${\rm A.D.I.}$ methods, SIAM J. Numer. Anal., 4 (1967), 163–170 10.1137/0704016 MR0218027 0252.65072 LinkGoogle Scholar[4] A. R. Gourlay and , A. R. 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Temam, Masters Thesis, Sur la stabilité et la convergence de la mèthode des pas fractionnaires, Doctoral thesis, University of Paris, Paris, 1967 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Analysis of a compact multi-step ADI method for linear parabolic equationInternational Journal of Modelling and Simulation, Vol. 40, No. 1 | 3 September 2018 Cross Ref Improved ADI Scheme for Linear Hyperbolic Equations: Extension to Nonlinear Cases and Compact ADI SchemesJournal of Scientific Computing, Vol. 72, No. 2 | 28 January 2017 Cross Ref Parabolic Partial Differential EquationsNumerical Solution of Partial Differential Equations in Science and Engineering | 25 February 2011 Cross Ref Elliptic Partial Differential EquationsNumerical Solution of Partial Differential Equations in Science and Engineering | 25 February 2011 Cross Ref Fundamental Schemes for Efficient Unconditionally Stable Implicit Finite-Difference Time-Domain MethodsIEEE Transactions on Antennas and Propagation, Vol. 56, No. 1 | 1 Jan 2008 Cross Ref A splitting up algorithm for the determination of the control parameter in multi dimensional parabolic problemApplied Mathematics and Computation, Vol. 166, No. 3 | 1 Jul 2005 Cross Ref A fractional splitting algorithm for nonoverlapping domain decomposition for parabolic problemNumerical Methods for Partial Differential Equations, Vol. 18, No. 5 | 21 August 2002 Cross Ref A Fractional Splitting Algorithm for Non-overlapping Domain DecompositionComputational Science — ICCS 2002 | 10 April 2002 Cross Ref Stability and convergence of the Peaceman-Rachford ADI method for initial-boundary value problemsMathematics of Computation, Vol. 53, No. 187 | 1 January 1989 Cross Ref Splitting methods for fourth order parabolic partial differential equationsComputing, Vol. 37, No. 4 | 1 Dec 1986 Cross Ref An analysis of alternating-direction methods for parabolic equationsNumerical Methods for Partial Differential Equations, Vol. 1, No. 1 | 1 Jan 1985 Cross Ref Chapter 13 Collocation Solution of the Transport Equation Using a Locally Enhanced Alternating Direction FormulationUnification of Finite Element Methods | 1 Jan 1984 Cross Ref Time Discretization in Parabolic EquationsNumerical Solution of Partial Differential Equations: Theory, Tools and Case Studies | 1 Jan 1983 Cross Ref Numerical solution of the atmospheric diffusion equation for chemically reacting flowsJournal of Computational Physics, Vol. 45, No. 1 | 1 Jan 1982 Cross Ref Recent developments of the hopscotch ideaConference on the Numerical Solution of Differential Equations | 28 August 2006 Cross Ref The hopscotch class of difference methods for partial differential equationsNumerische Lösung nichtlinearer partieller Differential- und Integrodifferentialgleichungen | 24 August 2006 Cross Ref Splitting methods in partial differential equationsAbhandlungen aus dem Mathematischen Seminar der Universität Hamburg, Vol. 36, No. 1 | 26 November 2013 Cross Ref Volume 6, Issue 1| 1969SIAM Journal on Numerical Analysis1-159 History Submitted:06 February 1968Published online:14 July 2006 InformationCopyright © 1969 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0706004Article page range:pp. 37-46ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics