research-article

A New Computational Procedure for A.D.I. Methods

Authors:

G. Fairweather,

A. R. MitchellAuthors Info & Claims

SIAM Journal on Numerical Analysis, Volume 4, Issue 2

Pages 163 - 170

https://doi.org/10.1137/0704016

Published: 01 June 1967 Publication History

Abstract

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References

[1]

Jim Douglas, Jr., Alternating direction methods for three space variables, Numer. Math., 4 (1962), 41–63

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Jim Douglas, Jr., H. H. Rachford, Jr., On the numerical solution of heat conduction problems in two and three space variables, Trans. Amer. Math. Soc., 82 (1956), 421–439

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E. G. Djakonov, On an application of difference splitting operators, Ž. Vyčisl. Mat. i Mat. Fiz., 3 (1963), 385–388

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E. G. Djakonov, Difference schemes with splitting operator for higher-dimensional non-stationary problems, Ž. Vyčisl. Mat. i Mat. Fiz., 2 (1962), 549–568

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G. Fairweather, A. R. Mitchell, A high accuracy alternating direction method for the wave equation, J. Inst. Math. Appl., 1 (1965), 309–316

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G. Fairweather, A. R. Mitchell, A new alternating direction method for parabolic equations in three space variables, J. Soc. Indust. Appl. Math., 13 (1965), 957–965

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G. Fairweather, Masters Thesis, Doctoral thesis, University of St. Andrews, St. Andrews, Scotland, 1965

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Milton Lees, Alternating direction methods for hyperbolic differential equations, J. Soc. Indust. Appl. Math., 10 (1962), 610–616

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A. R. Mitchell, G. Fairweather, Improved forms of the alternating direction methods of Douglas, Peaceman, and Rachford for solving parabolic and elliptic equations, Numer. Math., 6 (1964), 285–292

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D. W. Peaceman, H. H. Rachford, Jr., The numerical solution of parabolic and elliptic differential equations, J. Soc. Indust. Appl. Math., 3 (1955), 28–41

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Richard S. Varga, Matrix iterative analysis, Prentice-Hall Inc., Englewood Cliffs, N.J., 1962xiii+322

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Cited By

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Bialecki BFernandes R(2006)An Alternating-Direction Implicit Orthogonal Spline Collocation Scheme for Nonlinear Parabolic Problems on Rectangular PolygonsSIAM Journal on Scientific Computing10.1137/05062788528:3(1054-1077)Online publication date: 1-Jan-2006
https://dl.acm.org/doi/10.1137/050627885
Dendy, Jr. J(1977)An Alternating Direction Method for Schrödinger’s EquationSIAM Journal on Numerical Analysis10.1137/071407014:6(1028-1032)Online publication date: 1-Dec-1977
https://dl.acm.org/doi/10.1137/0714070
Dendy, Jr. J(1977)Alternating Direction Methods for Nonlinear Time-Dependent ProblemsSIAM Journal on Numerical Analysis10.1137/071402014:2(313-326)Online publication date: 1-Apr-1977
https://dl.acm.org/doi/10.1137/0714020
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Index Terms

A New Computational Procedure for A.D.I. Methods
1. Mathematics of computing
  1. Mathematical analysis
2. Theory of computation

Index terms have been assigned to the content through auto-classification.

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cover image SIAM Journal on Numerical Analysis

SIAM Journal on Numerical Analysis Volume 4, Issue 2

Jun 1967

185 pages

ISSN:0036-1429

DOI:10.1137/sjnaam.1967.4.issue-2

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Society for Industrial and Applied Mathematics

United States

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Published: 01 June 1967

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Bialecki BFernandes R(2006)An Alternating-Direction Implicit Orthogonal Spline Collocation Scheme for Nonlinear Parabolic Problems on Rectangular PolygonsSIAM Journal on Scientific Computing10.1137/05062788528:3(1054-1077)Online publication date: 1-Jan-2006
https://dl.acm.org/doi/10.1137/050627885
Dendy, Jr. J(1977)An Alternating Direction Method for Schrödinger’s EquationSIAM Journal on Numerical Analysis10.1137/071407014:6(1028-1032)Online publication date: 1-Dec-1977
https://dl.acm.org/doi/10.1137/0714070
Dendy, Jr. J(1977)Alternating Direction Methods for Nonlinear Time-Dependent ProblemsSIAM Journal on Numerical Analysis10.1137/071402014:2(313-326)Online publication date: 1-Apr-1977
https://dl.acm.org/doi/10.1137/0714020
Gourlay AMitchell A(1969)The Equivalence of Certain Alternating Direction and Locally One-Dimensional Difference MethodsSIAM Journal on Numerical Analysis10.1137/07060046:1(37-46)Online publication date: 1-Mar-1969
https://dl.acm.org/doi/10.1137/0706004

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On Computational Tools, Computational Thinking and Computational Methods

Kolmogorov Complexity and Computational Complexity

Computational complexity simplified

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