NUMERICAL STUDIES ON THE CONVERGENCE OF THE PEACEMAN-RACHFORD ALTERNATING DIRECTION IMPLICIT METHOD.

Abstract

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 Laplace's 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.

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1967
Accession Number
AD0654526

Entities

People

  • Alkis J. Mouradoglou

Organizations

  • University of Texas at Austin

Tags

DTIC Thesaurus Topics

  • Analogs
  • Computer Programs
  • Computers
  • Convergence
  • Difference Equations
  • Differential Equations
  • Equations
  • Iterations
  • Mathematical Analysis
  • Mathematics
  • Partial Differential Equations

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
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