A Note on Convergence of Line Iterative
Methods for a Nine-Point Matrix

Samir Karaa
Laboratiore MIP, UMR 5640, Universit\'e
Paul Sabatier, 118 route de Narbonne,
31062 Toulouse Cedex 4, France


Jun Zhang
Laboratory for High Performance Scientific Computing and Numerical Simulation
Department of Computer Science
University of Kentucky
773 Anderson Hall
Lexington, KY 40506-0046, USA


We prove the convergence of line iterative methods for solving the linear system arising from a 9-point compact discretization of a special two dimensional convection-diffusion equation. The results provide rigorous justification for the numerical experiments conducted elsewhere, which demonstrate the high accuracy and stability advantages of the fourth-order compact scheme.

Key words: Convection-diffusion equation, Fourth-order compact scheme, Linear systems, Line lterative methods, Spectral radius

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This paper has been published in Applied Mathematics Letters, Vol. 15, pp. 495-503 (2002). Technical Report No. 309-00, Department of Computer Science, University of Kentucky, Lexington, KY, 2000. The second author's research work was supported in part by the U.S. National Science Foundation under grants CCR-9902022, CCR-9988165 and CCR-0043861.