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On Difference Methods for Parabolic Equations and Alternating Direction Implicit Methods for Elliptic Equations

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1 Author(s)
Widlund, O.B. ; Department of Computer Sciences, University of Uppsala, Sweden

Some aspects are discussed of the development of the theory of difference approximations to parabolic equations in its relation to the basic development of difference methods for hyperbolic and elliptic equations by Courant, Friedrichs and Lewy, [Math. Ann. 100, 32 (1928)]. The present paper also deals with the related problem of establishing the convergence of alternating direction implicit methods for elliptic problems.

Note: The Institute of Electrical and Electronics Engineers, Incorporated is distributing this Article with permission of the International Business Machines Corporation (IBM) who is the exclusive owner. The recipient of this Article may not assign, sublicense, lease, rent or otherwise transfer, reproduce, prepare derivative works, publicly display or perform, or distribute the Article.  

Published in:

IBM Journal of Research and Development  (Volume:11 ,  Issue: 2 )