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The Solution of Elliptic Difference Equations by Semi-Explicit Iterative Techniques

Gunn, James E. (1965) The Solution of Elliptic Difference Equations by Semi-Explicit Iterative Techniques. Journal of the Society for Industrial and Applied Mathematics. Series B, Numerical analysis, 2 (1). pp. 24-45. ISSN 0887-459X. https://resolver.caltech.edu/CaltechAUTHORS:20120926-074835498

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Abstract

In [8], the author discusses an iterative scheme for solving a difference analogue for the elliptic differential equation ∇•α∇u = f on two-dimensional rectangular regions with Dirichlet boundary conditions. It is shown there that a semi-explicit technique involving the inversion only of the Peaceman-Rachford [10] alternating-direction operators for the Laplacian gives convergence in O(h^(-2) log h^(-1)) operations.


Item Type:Article
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http://dx.doi.org/10.1137/0702003DOIUNSPECIFIED
http://epubs.siam.org/doi/abs/10.1137/0702003PublisherUNSPECIFIED
Additional Information:© 1965 Society for Industrial and Applied Mathematics. Received by the editors January 6, 1964, and in revised form August 24, 1964. Published online: 03 August 2006. The author wishes to express thanks to D. N. Turner, who prepared the experimental programs and conducted most of the experiments.
Issue or Number:1
Record Number:CaltechAUTHORS:20120926-074835498
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20120926-074835498
Official Citation:The Solution of Elliptic Difference Equations by Semi-Explicit Iterative Techniques James E. Gunn Journal of the Society for Industrial and Applied Mathematics Series B Numerical Analysis 2-1 (1965), pp. 24-45http://dx.doi.org/10.1137/0702003
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:34381
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:26 Sep 2012 15:17
Last Modified:03 Oct 2019 04:18

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