Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

The method of Garabedian

Some extensions


In this paper, the method of Garabedian is applied to finite difference equations derived from the elliptic diffusion operator −D Δ +ɛ over rectangular and triangular nets. An example is given for which GARABEDIAN'S method yields a useless result.

This is a preview of subscription content, log in to check access.


  1. 1.

    De Meersman, R.: De Methode van Garabedian en aanverwante Problemen. Thesis. University of Brussels, 1965.

  2. 2.

    Forsythe, G. E., andW. R. Wasow: Finite-difference methods for partial differential equations. First edition. New York and London: John Wiley & Sons Inc. 1960.

  3. 3.

    Garabedian, P. R.: Estimation of the relaxation factor for small mesh size. Mathematical Tables and other Aids to Computation10, 183–185 (1956).

  4. 4.

    Habetler, G. J., andM. A. Martino: The multigroup diffusion equations of reactor physics. Knolls Atomic Power Laboratory. KAPL-1886, 1958 (report).

  5. 5.

    Martino, M. A.: Concerning the multigroup diffusion operator. Knolls Atomic Power Laboratory. KAPL-1867, 1957 (report).

  6. 6.

    Parter, S. V.: On estimating the rate of convergence of iterative methods for elliptic difference equations. Transactions of the American Mathematical Society114, 320–354 (1965).

  7. 7.

    Petrovsky, I. G.: Lectures on partial differential equations. First edition. New York: Interscience Publishers Inc. 1954.

  8. 8.

    Richtmyer, R. D.: Difference methods for initial value problems. First edition. New York: Interscience Publishers Inc. 1957

  9. 9.

    Varga, R. S.: Matrix iterative analysis. First edition. Englewood Cliffs, New Jersey: Prentice-Hall 1962.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

de Meersman, R. The method of Garabedian. Numer. Math. 11, 257–263 (1968).

Download citation


  • Finite Difference
  • Mathematical Method
  • Difference Equation
  • Diffusion Operator
  • Finite Difference Equation