A Note on Convergence of Line Iterative
Methods for a Nine-Point Matrix
Laboratiore MIP, UMR 5640, Universit\'e
Paul Sabatier, 118 route de Narbonne,
31062 Toulouse Cedex 4, France
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.
Convection-diffusion equation, Fourth-order
compact scheme, Linear systems, Line lterative methods,
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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.