NUMERICAL STUDIES ON THE CONVERGENCE OF THE PEACEMAN-RACHFORD ALTERNATING DIRECTION IMPLICIT METHOD.
Interim technical rept.,
TEXAS UNIV AUSTIN COMPUTATION CENTER
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The Peaceman-Rachford alternating direction implicit iterative method has proved to be a very effective method for solving difference equations arising in the solution of elliptic partial differential equations by finite difference methods, but no general proofs exist concerning the convergence for nonrectangular regions with several iteration parameters even for difference equations corresponding to Laplaces equation. The purpose of this paper is to describe some theoretical studies on the convergence properties of the Peaceman-Rachford method for solving the discrete analogue of the Dirichlet problem for nonrectangular regions. To facilitate these studies a computer program has been prepared for the Control Data 6600 computer.
- Numerical Mathematics