Abstract
The paper is concerned with the numerical solution of the initial boundary value problem for a class of multi-dimensional parabolic partial differential equations. In particular the time-integration of semi-discrete equations is investigated. An attempt is made to develop integration formulas being computationally attractive and of high accuracy, while possessing unconditional stability properties. To that end iterated defect correction is applied to the LOD method. The convergence properties of this process are investigated. Numerical experiments are reported.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. Abramowitz and I. A. Stegun,Handbook of mathematical functions, National Bureau of Standards Applied Mathematics Series 55, U.S. Government Printing Office, Washington, 1964.
R. Frank and C. W. Ueberhuber,Iterated defect correction for the efficient solution of stiff systems of ordinary differential equations, Report No. 17/76, Institute for Numerical Analysis, Technical University, Vienna, 1976 (in a condensed form published in BIT 17 (1977), 146–159).
H. J. Stetter,The defect correction principle and discretization methods, Num. Math. 29 (1978), 425–443.
P. J. van der Houwen and J. G. Verwer,One-step splitting methods formulated for semi-discrete parabolic equations, Report NW 55/78, Mathematisch Centrum, Amsterdam (prepublication) 1978 (to appear in Computing).
P. J. van der Houwen, B. P. Sommeijer and J. G. Verwer,Comparing time-integrators for parabolic equations in two space dimensions with a mixed derivative, J. of Comp. and Applied Math. 5, No. 2, 1979.
J. G. Verwer,The application of iterated defect correction to the LOD method for parabolic equations, Report NW 58/78, Mathematisch Centrum, Amsterdam, 1978.
N. N. Yanenko,The method of fractional steps, Springer-Verlag, Berlin, 1971.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Verwer, J.G. The application of iterated defect correction to theLod method for parabolic equations. BIT 19, 384–394 (1979). https://doi.org/10.1007/BF01930992
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01930992