BIT Numerical Mathematics

, Volume 12, Issue 1, pp 63–71 | Cite as

On the design of nested iterations for elliptic difference equations

  • Lydia Kronsjö
  • Germund Dahlquist
Article

Abstract

By “Richardson extrapolation from 2h andh toh/2” the results of computations with coarse grids are used for the construction of an initial approximation on finer grid. After a rather small number of iterations high accuracy is obtained. Numerical results are given for the two-dimensional Laplace equation.

Keywords

Computational Mathematic Difference Equation Initial Approximation Laplace Equation Coarse Grid 

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References

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    V. Pereyra,Accelerating the Convergence of Discretization Algorithms, SIAM J., Numer. Anal., Vol 4, No 4, 1967.Google Scholar
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    H. J. Stetter,Asymptotic Expansions for the Error of Discretization Algorithms for Non-Linear Functional Equations, Num. Math., 7, 1965.Google Scholar
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    E. L. Wachspress,Iterative Solution of Elliptic Systems and Applications to the Neutron Diffusion Equations of Reactor Physics, Prentice Hall.Google Scholar
  4. 4.
    B. Lindberg,Interpolation in the results of extrapolation methods for differential equations, submitted to SIAM Journal of Numerical Analysis.Google Scholar
  5. 5.
    N. S. Bahvalov,Convergence of a relaxation method under natural constraints on an elliptic operator, Z. Vycisl. Mat. i Mat. Fiz 6 (1966), 861–883. (Russian).Google Scholar

Copyright information

© BIT Foundations 1972

Authors and Affiliations

  • Lydia Kronsjö
    • 1
    • 2
  • Germund Dahlquist
    • 1
    • 2
  1. 1.Computer CentreUniversity of BirminghamBirminghamEngland
  2. 2.Department for Information ProcessingThe Royal Institute of TechnologyStockholm 70Sweden

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