A note on convergence of line iterative methods for a nine-point matrix

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Abstract

We prove the convergence of line iterative methods for solving the linear system arising from a nine-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. Numerical experiments are used to support our analytic results.

Keywords

Convection diffusion equation
Fourth-order compact scheme
Linear systems
Line Jacobi method
Spectral radius

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This author's research was supported by the U.S. National Science Foundation under Grants CCR-9902022, CCR-9988165, and CCR-0043861.