Numerische Mathematik

, Volume 10, Issue 1, pp 56–66 | Cite as

Some high accuracy difference schemes with a splitting operator for equations of parabolic and elliptic type

  • G. Fairweather
  • A. R. Gourlay
  • A. R. Mitchell
Article
Received:

Summary

High accuracy alternating direction implicit difference schemes for the heat equation, LAPLACE's equation and the biharmonic equation are considered. In addition to surveying the existing methods, several new methods are introduced. Sequences of iteration parameters are obtained for the elliptic problems and a numerical example is given.

Keywords

Mathematical Method Difference Scheme Heat Equation Elliptic Problem Accuracy Difference 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References

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    Conte, S. D., andR. T. Dames: An alternating direction method for solving the biharmonic equation. M.T.A.C.12, 998–205 (1958).Google Scholar
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    Mitchell, A. R., andG. Fairweather: Improved forms of the alternating direction methods of Douglas, Peaceman and Rachford for solving parabolic and elliptic equations. Numer. Math.6, 285–292 (1964).Google Scholar
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    Samarskii, A. A.: An accurate high order difference system for a heat conduction equation with several space variables. Z. Vycisl. Mat i Mat Fiz.4, 169–165 (1964).Google Scholar
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    ——, andV. B. Andreev: A difference scheme of higher accuracy for an equation of elliptic type in several space variables. Z. Vycisł. Mat i Mat Fiz.3, 1006–1013 (1963).Google Scholar

Copyright information

© Springer-Verlag 1967

Authors and Affiliations

  • G. Fairweather
    • 1
  • A. R. Gourlay
    • 1
  • A. R. Mitchell
    • 1
  1. 1.Department of Applied MathematicsSt. Andrews University FifeScotland

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