This is a preview of subscription content, log in via an institution to check access.
References
Bers, L.: On mildly nonlinear partial difference equations of elliptic type. J. Res. Nat. Bur. Stand.51, 229–236 (1953).
Birkhoff, G., andR. S. Varga: Implicit alternating direction methods. Trans. Amer. Math. Soc.92, 13–24 (1959).
Courant, R., andD. Hilbert: Methods of Mathematical Physics, vol I. New York: Interscience Publishers, Inc. 1953.
Douglas, J.: On the numerical integration of quasi-linear parabolic equations. Pacific J. Math.6, 35–42 (1956).
Douglas, J.: On the numerical integration ofu xx +u yy =u t by implicit methods. J. Soc. Industr Appl. Math.3, 42–65 (1955).
Douglas, J.: A note on the alternating direction implicit method for the numerical solution of heat conduction problem. Proc. Amer. Math. Soc.8, 409–412 (1957).
Douglas, J., andH. H. Rachford: On the numerical solution of heat conduction problems in two and three space variables. Trans. Amer. Math. Soc.82, 421–439 (1956).
Peaceman, D. W., andH. H. Rachford: The numerical solution of parabolic and elliptic differential equations. J. Soc. Indust. Appl. Math.3, 28–41 (1955).
Varga, R. S.: Iterative Numerical Analysis, University of Pittsburgh, 1959.
Wachspress, E. L., andG. J. Habetler: An alternating-direction-implicit iteration technique. J. Soc. Indust. Appl. Math.8, 403–423 (1960).
Young, D. M.: Iterative methods for solving partial difference equations of elliptic type. Trans. Amer. Math. Soc.76, 92–111 (1954).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Douglas, J. Alternating direction iteration for mildly nonlinear elliptic difference equations. Numer. Math. 3, 92–98 (1961). https://doi.org/10.1007/BF01386006
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01386006